Solve {l}{y=x+1}{z=-3x+4}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = x + 1 }\\ { z = -3 x + 4 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{4-a}{3}$$

$$y=\frac{7-a}{3}$$

$$z=a$$

Short Steps Using Substitution

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

$$x=-\frac{1}{3}z+\frac{4}{3} z=a$$

Substitute a for z in the equation x=-\frac{1}{3}z+\frac{4}{3}.

$$x=-\frac{1}{3}a+\frac{4}{3}$$

Substitute \frac{4}{3}-\frac{1}{3}a for x in the equation y=x+1.

$$y=\frac{4}{3}-\frac{1}{3}a+1$$

Calculate y from y=\frac{4}{3}-\frac{1}{3}a+1.

$$y=\frac{7}{3}-\frac{1}{3}a$$

The system is now solved.

$$x=-\frac{1}{3}a+\frac{4}{3} y=\frac{7}{3}-\frac{1}{3}a z=a$$