Solve {l}{x-7=5{(2x+3)}-13}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x - 7 = 5 {(2 x + 3)} - 13 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 5 by 2x+3.

$$x-7=10x+15-13$$

Subtract 13 from 15 to get 2.

$$x-7=10x+2$$

Subtract 10x from both sides.

$$x-7-10x=2$$

Combine x and -10x to get -9x.

$$-9x-7=2$$

Add 7 to both sides.

$$-9x=2+7$$

Add 2 and 7 to get 9.

$$-9x=9$$

Divide both sides by -9.

$$x=\frac{9}{-9}$$

Divide 9 by -9 to get -1.

$$x=-1$$

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

$$y=-1$$

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

$$z=-1$$

The system is now solved.

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