Solve {l}{75*6-8*100={(75+100)}x}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 75 \cdot 6 - 8 \cdot 100 = {(75 + 100)} x }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-2$$

Solution Steps

Consider the first equation. Multiply 75 and 6 to get 450.

$$450-8\times 100=\left(75+100\right)x$$

Multiply 8 and 100 to get 800.

$$450-800=\left(75+100\right)x$$

Subtract 800 from 450 to get -350.

$$-350=\left(75+100\right)x$$

Add 75 and 100 to get 175.

$$-350=175x$$

Swap sides so that all variable terms are on the left hand side.

$$175x=-350$$

Divide both sides by 175.

$$x=\frac{-350}{175}$$

Divide -350 by 175 to get -2.

$$x=-2$$

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

$$y=-2$$

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

$$z=-2$$

The system is now solved.

$$x=-2 y=-2 z=-2$$