Solve {l}{5-5x=-3{(2x+4)}}{y=7-{(-x+8)}+2{(4)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 - 5 x = -3 {(2 x + 4)} }\\ { y = 7 - {(-x + 8)} + 2 {(4)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-10$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -3 by 2x+4.

$$5-5x=-6x-12$$

Add 6x to both sides.

$$5-5x+6x=-12$$

Combine -5x and 6x to get x.

$$5+x=-12$$

Subtract 5 from both sides.

$$x=-12-5$$

Subtract 5 from -12 to get -17.

$$x=-17$$

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

$$y=7-\left(-\left(-17\right)+8\right)+2\times 4$$

The opposite of -17 is 17.

$$y=7-\left(17+8\right)+2\times 4$$

Add 17 and 8 to get 25.

$$y=7-25+2\times 4$$

Subtract 25 from 7 to get -18.

$$y=-18+2\times 4$$

Multiply 2 and 4 to get 8.

$$y=-18+8$$

Add -18 and 8 to get -10.

$$y=-10$$

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

$$z=-10$$

The system is now solved.

$$x=-17 y=-10 z=-10$$