Solve {l}{y=2x-1}{y=0}{z=5x+2}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = 2 x - 1 }\\ { y = 0 }\\ { z = 5 x + 2 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Solution Steps

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

$$0=2x-1$$

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

$$2x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$2x=1$$

Divide both sides by 2.

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

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

$$z=5\times \frac{1}{2}+2$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$z=\frac{5}{2}+2$$

Add \frac{5}{2} and 2 to get \frac{9}{2}.

$$z=\frac{9}{2}$$

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

$$a=\frac{9}{2}$$

The system is now solved.

$$y=0 x=\frac{1}{2} z=\frac{9}{2} a=\frac{9}{2}$$