Solve {l}{11*{(x-2)}=-3*{(x-7)}+3*{(5x+9)}}{y=20-20}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 11 \cdot {(x - 2)} = -3 \cdot {(x - 7)} + 3 \cdot {(5 x + 9)} }\\ { y = 20 - 20 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0$$

Solution Steps

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

$$11x-22=-3\left(x-7\right)+3\left(5x+9\right)$$

Use the distributive property to multiply -3 by x-7.

$$11x-22=-3x+21+3\left(5x+9\right)$$

Use the distributive property to multiply 3 by 5x+9.

$$11x-22=-3x+21+15x+27$$

Combine -3x and 15x to get 12x.

$$11x-22=12x+21+27$$

Add 21 and 27 to get 48.

$$11x-22=12x+48$$

Subtract 12x from both sides.

$$11x-22-12x=48$$

Combine 11x and -12x to get -x.

$$-x-22=48$$

Add 22 to both sides.

$$-x=48+22$$

Add 48 and 22 to get 70.

$$-x=70$$

Divide both sides by -1.

$$x=-70$$

Consider the second equation. Subtract 20 from 20 to get 0.

$$y=0$$

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

$$z=0$$

The system is now solved.

$$x=-70 y=0 z=0$$