Solve {l}{3(x+2x+2)/4=4x+y-1/3}{1/3(x+y-1/6(x-y)=frac{y-1}{6}}

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

Solve for x

$$x=\frac{4y}{11}-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\times 3\left(x+2x+2\right)=4\left(4x+y-1\right)$$

Multiply 3 and 3 to get 9.

$$9\left(x+2x+2\right)=4\left(4x+y-1\right)$$

Combine x and 2x to get 3x.

$$9\left(3x+2\right)=4\left(4x+y-1\right)$$

Use the distributive property to multiply 9 by 3x+2.

$$27x+18=4\left(4x+y-1\right)$$

Use the distributive property to multiply 4 by 4x+y-1.

$$27x+18=16x+4y-4$$

Subtract 16x from both sides.

$$27x+18-16x=4y-4$$

Combine 27x and -16x to get 11x.

$$11x+18=4y-4$$

Subtract 18 from both sides.

$$11x=4y-4-18$$

Subtract 18 from -4 to get -22.

$$11x=4y-22$$

Divide both sides by 11.

$$\frac{11x}{11}=\frac{4y-22}{11}$$

Dividing by 11 undoes the multiplication by 11.

$$x=\frac{4y-22}{11}$$

Divide 4y-22 by 11.

$$x=\frac{4y}{11}-2$$