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

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

Solve for x, y, z

$$z = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Solution Steps

Consider the first equation. Combine 7x and -x to get 6x.

$$6x-4=-2x+8$$

Add 2x to both sides.

$$6x-4+2x=8$$

Combine 6x and 2x to get 8x.

$$8x-4=8$$

Add 4 to both sides.

$$8x=8+4$$

Add 8 and 4 to get 12.

$$8x=12$$

Divide both sides by 8.

$$x=\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{3}{2}$$

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

$$y=-3\times \frac{3}{2}$$

Multiply -3 and \frac{3}{2} to get -\frac{9}{2}.

$$y=-\frac{9}{2}$$

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

$$z=-\frac{9}{2}$$

The system is now solved.

$$x=\frac{3}{2} y=-\frac{9}{2} z=-\frac{9}{2}$$