Solve {l}{13=-4x+6}{y=x+7}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 13 = -4 x + 6 }\\ { y = x + 7 }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

Solution Steps

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

$$-4x+6=13$$

Subtract 6 from both sides.

$$-4x=13-6$$

Subtract 6 from 13 to get 7.

$$-4x=7$$

Divide both sides by -4.

$$x=-\frac{7}{4}$$

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

$$y=-\frac{7}{4}+7$$

Add -\frac{7}{4} and 7 to get \frac{21}{4}.

$$y=\frac{21}{4}$$

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

$$z=\frac{21}{4}$$

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

$$a=\frac{21}{4}$$

The system is now solved.

$$x=-\frac{7}{4} y=\frac{21}{4} z=\frac{21}{4} a=\frac{21}{4}$$