Solve {l}{2x+4y=-2}{z=1501y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 2 x + 4 y = -2 }\\ { z = 1501 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=-\frac{2a}{1501}-1$$

$$y=\frac{a}{1501}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=1501y 2x+4y=-2 a=z$$

Substitute 1501y for z in the equation a=z.

$$a=1501y$$

Solve the second equation for x and the third equation for y.

$$x=-1-2y y=\frac{1}{1501}a$$

Substitute \frac{1}{1501}a for y in the equation x=-1-2y.

$$x=-1-2\times \frac{1}{1501}a$$

Calculate x from x=-1-2\times \frac{1}{1501}a.

$$x=-1-\frac{2}{1501}a$$

Substitute \frac{1}{1501}a for y in the equation z=1501y.

$$z=1501\times \frac{1}{1501}a$$

Calculate z from z=1501\times \frac{1}{1501}a.

$$z=a$$

The system is now solved.

$$x=-1-\frac{2}{1501}a y=\frac{1}{1501}a z=a$$