Solve {l}{y=1/2x+2}{y=-1}{z=5x-2}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = \frac{1}{2} x + 2 }\\ { y = -1 }\\ { z = 5 x - 2 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a=-32$$

Solution Steps

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

$$-1=\frac{1}{2}x+2$$

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

$$\frac{1}{2}x+2=-1$$

Subtract 2 from both sides.

$$\frac{1}{2}x=-1-2$$

Subtract 2 from -1 to get -3.

$$\frac{1}{2}x=-3$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=-3\times 2$$

Multiply -3 and 2 to get -6.

$$x=-6$$

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

$$z=5\left(-6\right)-2$$

Multiply 5 and -6 to get -30.

$$z=-30-2$$

Subtract 2 from -30 to get -32.

$$z=-32$$

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

$$a=-32$$

The system is now solved.

$$y=-1 x=-6 z=-32 a=-32$$