Solve {l}{7x-3y/3+2x-y/2=-x-2x+y/2}{2x-y-1/5+frac{x-2y+6}{15}+1=frac{3x-y+4}{3}}

$$\left\{ \begin{array} { l } { \frac { 7 x - 3 y } { 3 } + \frac { 2 x - y } { 2 } = - x - \frac { 2 x + y } { 2 } } \\ { \frac { 2 x - y - 1 } { 5 } + \frac { x - 2 y + 6 } { 15 } + 1 = \frac { 3 x - y + 4 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x=-\frac{1}{4}=-0.25$$

$$y = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(7x-3y\right)+3\left(2x-y\right)=-6x-3\left(2x+y\right)$$

Use the distributive property to multiply 2 by 7x-3y.

$$14x-6y+3\left(2x-y\right)=-6x-3\left(2x+y\right)$$

Use the distributive property to multiply 3 by 2x-y.

$$14x-6y+6x-3y=-6x-3\left(2x+y\right)$$

Combine 14x and 6x to get 20x.

$$20x-6y-3y=-6x-3\left(2x+y\right)$$

Combine -6y and -3y to get -9y.

$$20x-9y=-6x-3\left(2x+y\right)$$

Use the distributive property to multiply -3 by 2x+y.

$$20x-9y=-6x-6x-3y$$

Combine -6x and -6x to get -12x.

$$20x-9y=-12x-3y$$

Add 12x to both sides.

$$20x-9y+12x=-3y$$

Combine 20x and 12x to get 32x.

$$32x-9y=-3y$$

Add 3y to both sides.

$$32x-9y+3y=0$$

Combine -9y and 3y to get -6y.

$$32x-6y=0$$

Consider the second equation. Multiply both sides of the equation by 15, the least common multiple of 5,15,3.

$$3\left(2x-y-1\right)+x-2y+6+15=5\left(3x-y+4\right)$$

Use the distributive property to multiply 3 by 2x-y-1.

$$6x-3y-3+x-2y+6+15=5\left(3x-y+4\right)$$

Combine 6x and x to get 7x.

$$7x-3y-3-2y+6+15=5\left(3x-y+4\right)$$

Combine -3y and -2y to get -5y.

$$7x-5y-3+6+15=5\left(3x-y+4\right)$$

Add -3 and 6 to get 3.

$$7x-5y+3+15=5\left(3x-y+4\right)$$

Add 3 and 15 to get 18.

$$7x-5y+18=5\left(3x-y+4\right)$$

Use the distributive property to multiply 5 by 3x-y+4.

$$7x-5y+18=15x-5y+20$$

Subtract 15x from both sides.

$$7x-5y+18-15x=-5y+20$$

Combine 7x and -15x to get -8x.

$$-8x-5y+18=-5y+20$$

Add 5y to both sides.

$$-8x-5y+18+5y=20$$

Combine -5y and 5y to get 0.

$$-8x+18=20$$

Subtract 18 from both sides.

$$-8x=20-18$$

Subtract 18 from 20 to get 2.

$$-8x=2$$

Divide both sides by -8.

$$x=\frac{2}{-8}$$

Reduce the fraction \frac{2}{-8} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{4}$$

Consider the first equation. Insert the known values of variables into the equation.

$$32\left(-\frac{1}{4}\right)-6y=0$$

Multiply 32 and -\frac{1}{4} to get -8.

$$-8-6y=0$$

Add 8 to both sides. Anything plus zero gives itself.

$$-6y=8$$

Divide both sides by -6.

$$y=\frac{8}{-6}$$

Reduce the fraction \frac{8}{-6} to lowest terms by extracting and canceling out 2.

$$y=-\frac{4}{3}$$

The system is now solved.

$$x=-\frac{1}{4} y=-\frac{4}{3}$$