Solve {l}{7x-6/4=9}{y=7-2x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{7 x - 6}{4} = 9 }\\ { y = 7 - 2 x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-5$$

Solution Steps

Consider the first equation. Multiply both sides by 4.

$$7x-6=9\times 4$$

Multiply 9 and 4 to get 36.

$$7x-6=36$$

Add 6 to both sides.

$$7x=36+6$$

Add 36 and 6 to get 42.

$$7x=42$$

Divide both sides by 7.

$$x=\frac{42}{7}$$

Divide 42 by 7 to get 6.

$$x=6$$

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

$$y=7-2\times 6$$

Multiply -2 and 6 to get -12.

$$y=7-12$$

Subtract 12 from 7 to get -5.

$$y=-5$$

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

$$z=-5$$

The system is now solved.

$$x=6 y=-5 z=-5$$