Solve {l}{b/2x-frac{sqrt{3}}{2}*b*y=-frac{sqrt{3}}{2}*b^2}{b/2-x-y*b(1-frac{sqrt{3}}{2})=-a*b/2}

$$\left\{ \begin{array} { l } { \frac { b } { 2 } x - \frac { \sqrt { 3 } } { 2 } \cdot b \cdot y = - \frac { \sqrt { 3 } } { 2 } \cdot b ^ { 2 } } \\ { \frac { b } { 2 } - x - y \cdot b ( 1 - \frac { \sqrt { 3 } } { 2 } ) = - \frac { a \cdot b } { 2 } } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}\text{, }y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}\text{, }&b\neq -4\sqrt{3}-6\\x=\frac{b\left(\sqrt{3}y+a-2y+1\right)}{2}\text{, }y\in \mathrm{C}\text{, }&b=0\text{ or }\left(a=-2\sqrt{3}-1\text{ and }b=-4\sqrt{3}-6\right)\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Multiply both sides of the equation by 2.

$$bx-\sqrt{3}by=2\left(-\frac{\sqrt{3}}{2}\right)b^{2}$$

Express 2\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$bx-\sqrt{3}by=\frac{-2\sqrt{3}}{2}b^{2}$$

Cancel out 2 and 2.

$$bx-\sqrt{3}by=-\sqrt{3}b^{2}$$

Consider the second equation. Multiply both sides of the equation by 2.

$$2\left(\frac{b}{2}-x\right)-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Use the distributive property to multiply 2 by \frac{b}{2}-x.

$$2\times \frac{b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Express 2\times \frac{b}{2} as a single fraction.

$$\frac{2b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Cancel out 2 and 2.

$$b-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Multiply both sides of the equation by 2.

$$2\left(b-2x\right)-4yb\left(1-\frac{\sqrt{3}}{2}\right)=-2ab$$

Reorder the terms.

$$2\left(-2x+b\right)-4\left(-\frac{\sqrt{3}}{2}+1\right)by=-2ab$$

Multiply both sides of the equation by 2.

$$4\left(-2x+b\right)-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply 4 by -2x+b.

$$-8x+4b-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Multiply -2 and 4 to get -8.

$$-8x+4b-8\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply -8 by -\frac{\sqrt{3}}{2}+1.

$$-8x+4b+\left(8\times \frac{\sqrt{3}}{2}-8\right)by=-4ab$$

Cancel out 2, the greatest common factor in 8 and 2.

$$-8x+4b+\left(4\sqrt{3}-8\right)by=-4ab$$

Use the distributive property to multiply 4\sqrt{3}-8 by b.

$$-8x+4b+\left(4\sqrt{3}b-8b\right)y=-4ab$$

Use the distributive property to multiply 4\sqrt{3}b-8b by y.

$$-8x+4b+4\sqrt{3}by-8by=-4ab$$

Subtract 4b from both sides.

$$-8x+4\sqrt{3}by-8by=-4ab-4b$$

Combine all terms containing x,y.

$$-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2},-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2}$$

Add \sqrt{3}by to both sides of the equation.

$$bx=\sqrt{3}by-\sqrt{3}b^{2}$$

Divide both sides by b.

$$x=\frac{1}{b}\left(\sqrt{3}by-\sqrt{3}b^{2}\right)$$

Multiply \frac{1}{b} times b\left(y-b\right)\sqrt{3}.

$$x=\sqrt{3}y-\sqrt{3}b$$

Substitute \left(y-b\right)\sqrt{3} for x in the other equation, -8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b.

$$-8\left(\sqrt{3}y-\sqrt{3}b\right)+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Multiply -8 times \left(y-b\right)\sqrt{3}.

$$\left(-8\sqrt{3}\right)y+8\sqrt{3}b+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Add -8\sqrt{3}y to 4b\left(\sqrt{3}-2\right)y.

$$\left(4\left(\sqrt{3}-2\right)b-8\sqrt{3}\right)y+8\sqrt{3}b=-4ab-4b$$

Subtract 8\sqrt{3}b from both sides of the equation.

$$\left(4\left(\sqrt{3}-2\right)b-8\sqrt{3}\right)y=-4b\left(a+2\sqrt{3}+1\right)$$

Divide both sides by -8\sqrt{3}+4b\left(\sqrt{3}-2\right).

$$y=-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

Substitute -\frac{b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b} for y in x=\sqrt{3}y-\sqrt{3}b. Because the resulting equation contains only one variable, you can solve for x directly.

$$x=\sqrt{3}\left(-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}\right)-\sqrt{3}b$$

Multiply \sqrt{3} times -\frac{b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b}.

$$x=-\frac{\sqrt{3}b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}-\sqrt{3}b$$

Add -\sqrt{3}b to -\frac{\sqrt{3}b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b}.

$$x=\frac{\sqrt{3}b\left(-\sqrt{3}b+2b-a-1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

The system is now solved.

$$x=\frac{\sqrt{3}b\left(-\sqrt{3}b+2b-a-1\right)}{\sqrt{3}b-2b-2\sqrt{3}},y=-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

Steps Using Elimination

Consider the first equation. Multiply both sides of the equation by 2.

$$bx-\sqrt{3}by=2\left(-\frac{\sqrt{3}}{2}\right)b^{2}$$

Express 2\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$bx-\sqrt{3}by=\frac{-2\sqrt{3}}{2}b^{2}$$

Cancel out 2 and 2.

$$bx-\sqrt{3}by=-\sqrt{3}b^{2}$$

Consider the second equation. Multiply both sides of the equation by 2.

$$2\left(\frac{b}{2}-x\right)-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Use the distributive property to multiply 2 by \frac{b}{2}-x.

$$2\times \frac{b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Express 2\times \frac{b}{2} as a single fraction.

$$\frac{2b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Cancel out 2 and 2.

$$b-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Multiply both sides of the equation by 2.

$$2\left(b-2x\right)-4yb\left(1-\frac{\sqrt{3}}{2}\right)=-2ab$$

Reorder the terms.

$$2\left(-2x+b\right)-4\left(-\frac{\sqrt{3}}{2}+1\right)by=-2ab$$

Multiply both sides of the equation by 2.

$$4\left(-2x+b\right)-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply 4 by -2x+b.

$$-8x+4b-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Multiply -2 and 4 to get -8.

$$-8x+4b-8\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply -8 by -\frac{\sqrt{3}}{2}+1.

$$-8x+4b+\left(8\times \frac{\sqrt{3}}{2}-8\right)by=-4ab$$

Cancel out 2, the greatest common factor in 8 and 2.

$$-8x+4b+\left(4\sqrt{3}-8\right)by=-4ab$$

Use the distributive property to multiply 4\sqrt{3}-8 by b.

$$-8x+4b+\left(4\sqrt{3}b-8b\right)y=-4ab$$

Use the distributive property to multiply 4\sqrt{3}b-8b by y.

$$-8x+4b+4\sqrt{3}by-8by=-4ab$$

Subtract 4b from both sides.

$$-8x+4\sqrt{3}by-8by=-4ab-4b$$

Combine all terms containing x,y.

$$-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2},-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

To make bx and -8x equal, multiply all terms on each side of the first equation by -8 and all terms on each side of the second by b.

$$-8bx-8\left(-\sqrt{3}b\right)y=-8\left(-\sqrt{3}b^{2}\right),b\left(-8\right)x+b\left(4\sqrt{3}b-8b\right)y=b\left(-4ab-4b\right)$$

Simplify.

$$\left(-8b\right)x+8\sqrt{3}by=8\sqrt{3}b^{2},\left(-8b\right)x+4\left(\sqrt{3}-2\right)b^{2}y=-4\left(a+1\right)b^{2}$$

Subtract \left(-8b\right)x+4\left(\sqrt{3}-2\right)b^{2}y=-4\left(a+1\right)b^{2} from \left(-8b\right)x+8\sqrt{3}by=8\sqrt{3}b^{2} by subtracting like terms on each side of the equal sign.

$$\left(-8b\right)x+8bx+8\sqrt{3}by+\left(-4\left(\sqrt{3}-2\right)b^{2}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add -8bx to 8bx. Terms -8bx and 8bx cancel out, leaving an equation with only one variable that can be solved.

$$8\sqrt{3}by+\left(-4\left(\sqrt{3}-2\right)b^{2}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add 8\sqrt{3}by to -4\left(\sqrt{3}-2\right)b^{2}y.

$$4b\left(-\left(\sqrt{3}-2\right)b+2\sqrt{3}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add 8\sqrt{3}b^{2} to 4\left(1+a\right)b^{2}.

$$4b\left(-\left(\sqrt{3}-2\right)b+2\sqrt{3}\right)y=4\left(a+2\sqrt{3}+1\right)b^{2}$$

Divide both sides by 4b\left(2\sqrt{3}-\left(\sqrt{3}-2\right)b\right).

$$y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

Substitute \frac{\left(2\sqrt{3}+1+a\right)b}{2\sqrt{3}-\sqrt{3}b+2b} for y in -8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b. Because the resulting equation contains only one variable, you can solve for x directly.

$$-8x+\left(4\sqrt{3}b-8b\right)\times \frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}=-4ab-4b$$

Multiply 4\sqrt{3}b-8b times \frac{\left(2\sqrt{3}+1+a\right)b}{2\sqrt{3}-\sqrt{3}b+2b}.

$$-8x+\frac{4\left(\sqrt{3}-2\right)\left(a+2\sqrt{3}+1\right)b^{2}}{-\sqrt{3}b+2b+2\sqrt{3}}=-4ab-4b$$

Subtract \frac{4\left(\sqrt{3}-2\right)\left(2\sqrt{3}+1+a\right)b^{2}}{2\sqrt{3}-\sqrt{3}b+2b} from both sides of the equation.

$$-8x=\frac{8b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

Divide both sides by -8.

$$x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

The system is now solved.

$$x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}},y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

Solve for x, y

$$\left\{\begin{matrix}x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}\text{, }y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}\text{, }&b\neq -4\sqrt{3}-6\\x=\frac{b\left(\sqrt{3}y+a-2y+1\right)}{2}\text{, }y\in \mathrm{R}\text{, }&b=0\text{ or }\left(a=-2\sqrt{3}-1\text{ and }b=-4\sqrt{3}-6\right)\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Multiply both sides of the equation by 2.

$$bx-\sqrt{3}by=2\left(-\frac{\sqrt{3}}{2}\right)b^{2}$$

Express 2\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$bx-\sqrt{3}by=\frac{-2\sqrt{3}}{2}b^{2}$$

Cancel out 2 and 2.

$$bx-\sqrt{3}by=-\sqrt{3}b^{2}$$

Consider the second equation. Multiply both sides of the equation by 2.

$$2\left(\frac{b}{2}-x\right)-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Use the distributive property to multiply 2 by \frac{b}{2}-x.

$$2\times \frac{b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Express 2\times \frac{b}{2} as a single fraction.

$$\frac{2b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Cancel out 2 and 2.

$$b-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Multiply both sides of the equation by 2.

$$2\left(b-2x\right)-4yb\left(1-\frac{\sqrt{3}}{2}\right)=-2ab$$

Reorder the terms.

$$2\left(-2x+b\right)-4\left(-\frac{\sqrt{3}}{2}+1\right)by=-2ab$$

Multiply both sides of the equation by 2.

$$4\left(-2x+b\right)-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply 4 by -2x+b.

$$-8x+4b-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Multiply -2 and 4 to get -8.

$$-8x+4b-8\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply -8 by -\frac{\sqrt{3}}{2}+1.

$$-8x+4b+\left(8\times \frac{\sqrt{3}}{2}-8\right)by=-4ab$$

Cancel out 2, the greatest common factor in 8 and 2.

$$-8x+4b+\left(4\sqrt{3}-8\right)by=-4ab$$

Use the distributive property to multiply 4\sqrt{3}-8 by b.

$$-8x+4b+\left(4\sqrt{3}b-8b\right)y=-4ab$$

Use the distributive property to multiply 4\sqrt{3}b-8b by y.

$$-8x+4b+4\sqrt{3}by-8by=-4ab$$

Subtract 4b from both sides.

$$-8x+4\sqrt{3}by-8by=-4ab-4b$$

Combine all terms containing x,y.

$$-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2},-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2}$$

Add \sqrt{3}by to both sides of the equation.

$$bx=\sqrt{3}by-\sqrt{3}b^{2}$$

Divide both sides by b.

$$x=\frac{1}{b}\left(\sqrt{3}by-\sqrt{3}b^{2}\right)$$

Multiply \frac{1}{b} times b\left(y-b\right)\sqrt{3}.

$$x=\sqrt{3}y-\sqrt{3}b$$

Substitute \left(y-b\right)\sqrt{3} for x in the other equation, -8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b.

$$-8\left(\sqrt{3}y-\sqrt{3}b\right)+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Multiply -8 times \left(y-b\right)\sqrt{3}.

$$\left(-8\sqrt{3}\right)y+8\sqrt{3}b+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

Add -8\sqrt{3}y to 4b\left(\sqrt{3}-2\right)y.

$$\left(4\left(\sqrt{3}-2\right)b-8\sqrt{3}\right)y+8\sqrt{3}b=-4ab-4b$$

Subtract 8\sqrt{3}b from both sides of the equation.

$$\left(4\left(\sqrt{3}-2\right)b-8\sqrt{3}\right)y=-4b\left(a+2\sqrt{3}+1\right)$$

Divide both sides by -8\sqrt{3}+4b\left(\sqrt{3}-2\right).

$$y=-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

Substitute -\frac{b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b} for y in x=\sqrt{3}y-\sqrt{3}b. Because the resulting equation contains only one variable, you can solve for x directly.

$$x=\sqrt{3}\left(-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}\right)-\sqrt{3}b$$

Multiply \sqrt{3} times -\frac{b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b}.

$$x=-\frac{\sqrt{3}b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}-\sqrt{3}b$$

Add -\sqrt{3}b to -\frac{\sqrt{3}b\left(a+1+2\sqrt{3}\right)}{-2\sqrt{3}+b\sqrt{3}-2b}.

$$x=\frac{\sqrt{3}b\left(-\sqrt{3}b+2b-a-1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

The system is now solved.

$$x=\frac{\sqrt{3}b\left(-\sqrt{3}b+2b-a-1\right)}{\sqrt{3}b-2b-2\sqrt{3}},y=-\frac{b\left(a+2\sqrt{3}+1\right)}{\sqrt{3}b-2b-2\sqrt{3}}$$

Steps Using Elimination

Consider the first equation. Multiply both sides of the equation by 2.

$$bx-\sqrt{3}by=2\left(-\frac{\sqrt{3}}{2}\right)b^{2}$$

Express 2\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$bx-\sqrt{3}by=\frac{-2\sqrt{3}}{2}b^{2}$$

Cancel out 2 and 2.

$$bx-\sqrt{3}by=-\sqrt{3}b^{2}$$

Consider the second equation. Multiply both sides of the equation by 2.

$$2\left(\frac{b}{2}-x\right)-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Use the distributive property to multiply 2 by \frac{b}{2}-x.

$$2\times \frac{b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Express 2\times \frac{b}{2} as a single fraction.

$$\frac{2b}{2}-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Cancel out 2 and 2.

$$b-2x-2yb\left(1-\frac{\sqrt{3}}{2}\right)=-ab$$

Multiply both sides of the equation by 2.

$$2\left(b-2x\right)-4yb\left(1-\frac{\sqrt{3}}{2}\right)=-2ab$$

Reorder the terms.

$$2\left(-2x+b\right)-4\left(-\frac{\sqrt{3}}{2}+1\right)by=-2ab$$

Multiply both sides of the equation by 2.

$$4\left(-2x+b\right)-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply 4 by -2x+b.

$$-8x+4b-2\times 4\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Multiply -2 and 4 to get -8.

$$-8x+4b-8\left(-\frac{\sqrt{3}}{2}+1\right)by=-4ab$$

Use the distributive property to multiply -8 by -\frac{\sqrt{3}}{2}+1.

$$-8x+4b+\left(8\times \frac{\sqrt{3}}{2}-8\right)by=-4ab$$

Cancel out 2, the greatest common factor in 8 and 2.

$$-8x+4b+\left(4\sqrt{3}-8\right)by=-4ab$$

Use the distributive property to multiply 4\sqrt{3}-8 by b.

$$-8x+4b+\left(4\sqrt{3}b-8b\right)y=-4ab$$

Use the distributive property to multiply 4\sqrt{3}b-8b by y.

$$-8x+4b+4\sqrt{3}by-8by=-4ab$$

Subtract 4b from both sides.

$$-8x+4\sqrt{3}by-8by=-4ab-4b$$

Combine all terms containing x,y.

$$-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

$$bx+\left(-\sqrt{3}b\right)y=-\sqrt{3}b^{2},-8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b$$

To make bx and -8x equal, multiply all terms on each side of the first equation by -8 and all terms on each side of the second by b.

$$-8bx-8\left(-\sqrt{3}b\right)y=-8\left(-\sqrt{3}b^{2}\right),b\left(-8\right)x+b\left(4\sqrt{3}b-8b\right)y=b\left(-4ab-4b\right)$$

Simplify.

$$\left(-8b\right)x+8\sqrt{3}by=8\sqrt{3}b^{2},\left(-8b\right)x+4\left(\sqrt{3}-2\right)b^{2}y=-4\left(a+1\right)b^{2}$$

Subtract \left(-8b\right)x+4\left(\sqrt{3}-2\right)b^{2}y=-4\left(a+1\right)b^{2} from \left(-8b\right)x+8\sqrt{3}by=8\sqrt{3}b^{2} by subtracting like terms on each side of the equal sign.

$$\left(-8b\right)x+8bx+8\sqrt{3}by+\left(-4\left(\sqrt{3}-2\right)b^{2}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add -8bx to 8bx. Terms -8bx and 8bx cancel out, leaving an equation with only one variable that can be solved.

$$8\sqrt{3}by+\left(-4\left(\sqrt{3}-2\right)b^{2}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add 8\sqrt{3}by to -4\left(\sqrt{3}-2\right)b^{2}y.

$$4b\left(-\left(\sqrt{3}-2\right)b+2\sqrt{3}\right)y=8\sqrt{3}b^{2}+4\left(a+1\right)b^{2}$$

Add 8\sqrt{3}b^{2} to 4\left(1+a\right)b^{2}.

$$4b\left(-\left(\sqrt{3}-2\right)b+2\sqrt{3}\right)y=4\left(a+2\sqrt{3}+1\right)b^{2}$$

Divide both sides by 4b\left(2\sqrt{3}-\left(\sqrt{3}-2\right)b\right).

$$y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

Substitute \frac{\left(2\sqrt{3}+1+a\right)b}{2\sqrt{3}-\sqrt{3}b+2b} for y in -8x+\left(4\sqrt{3}b-8b\right)y=-4ab-4b. Because the resulting equation contains only one variable, you can solve for x directly.

$$-8x+\left(4\sqrt{3}b-8b\right)\times \frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}=-4ab-4b$$

Multiply 4\sqrt{3}b-8b times \frac{\left(2\sqrt{3}+1+a\right)b}{2\sqrt{3}-\sqrt{3}b+2b}.

$$-8x+\frac{4\left(\sqrt{3}-2\right)\left(a+2\sqrt{3}+1\right)b^{2}}{-\sqrt{3}b+2b+2\sqrt{3}}=-4ab-4b$$

Subtract \frac{4\left(\sqrt{3}-2\right)\left(2\sqrt{3}+1+a\right)b^{2}}{2\sqrt{3}-\sqrt{3}b+2b} from both sides of the equation.

$$-8x=\frac{8b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

Divide both sides by -8.

$$x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$

The system is now solved.

$$x=-\frac{b\left(2\sqrt{3}b-\sqrt{3}a-3b-\sqrt{3}\right)}{-\sqrt{3}b+2b+2\sqrt{3}},y=\frac{b\left(a+2\sqrt{3}+1\right)}{-\sqrt{3}b+2b+2\sqrt{3}}$$