Solve {l}{14x+4=5x+31}{y=-5x-5x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 14 x + 4 = 5 x + 31 }\\ { y = -5 x - 5 x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-30$$

Solution Steps

Consider the first equation. Subtract 5x from both sides.

$$14x+4-5x=31$$

Combine 14x and -5x to get 9x.

$$9x+4=31$$

Subtract 4 from both sides.

$$9x=31-4$$

Subtract 4 from 31 to get 27.

$$9x=27$$

Divide both sides by 9.

$$x=\frac{27}{9}$$

Divide 27 by 9 to get 3.

$$x=3$$

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

$$y=-5\times 3-5\times 3$$

Do the multiplications.

$$y=-15-15$$

Subtract 15 from -15 to get -30.

$$y=-30$$

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

$$z=-30$$

The system is now solved.

$$x=3 y=-30 z=-30$$