Solve {l}{7+2x=4{(-x+2)}-31}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 + 2 x = 4 {(-x + 2)} - 31 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-5$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4 by -x+2.

$$7+2x=4\left(-x\right)+8-31$$

Subtract 31 from 8 to get -23.

$$7+2x=4\left(-x\right)-23$$

Subtract 4\left(-x\right) from both sides.

$$7+2x-4\left(-x\right)=-23$$

Multiply -1 and 4 to get -4.

$$7+2x-4\left(-1\right)x=-23$$

Multiply -4 and -1 to get 4.

$$7+2x+4x=-23$$

Combine 2x and 4x to get 6x.

$$7+6x=-23$$

Subtract 7 from both sides.

$$6x=-23-7$$

Subtract 7 from -23 to get -30.

$$6x=-30$$

Divide both sides by 6.

$$x=\frac{-30}{6}$$

Divide -30 by 6 to get -5.

$$x=-5$$

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

$$y=-5$$

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

$$z=-5$$

The system is now solved.

$$x=-5 y=-5 z=-5$$