Solve {l}{3{(12-x)}-4x=2{(11-x)}+9x}{y=1}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 3 {(12 - x)} - 4 x = 2 {(11 - x)} + 9 x }\\ { y = 1 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by 12-x.

$$36-3x-4x=2\left(11-x\right)+9x$$

Combine -3x and -4x to get -7x.

$$36-7x=2\left(11-x\right)+9x$$

Use the distributive property to multiply 2 by 11-x.

$$36-7x=22-2x+9x$$

Combine -2x and 9x to get 7x.

$$36-7x=22+7x$$

Subtract 7x from both sides.

$$36-7x-7x=22$$

Combine -7x and -7x to get -14x.

$$36-14x=22$$

Subtract 36 from both sides.

$$-14x=22-36$$

Subtract 36 from 22 to get -14.

$$-14x=-14$$

Divide both sides by -14.

$$x=\frac{-14}{-14}$$

Divide -14 by -14 to get 1.

$$x=1$$

The system is now solved.

$$x=1 y=1 z=1$$