Solve {l}{20x=5}{y=10+x}{z=x}{text{Solvefor}a,btext{where}}{a=y}{b=z}

$$\left. \begin{array} { l } { 20 x = 5 }\\ { y = 10 + x }\\ { z = x }\\ { \text{Solve for } a,b \text{ where} } \\ { a = y }\\ { b = z } \end{array} \right.$$

Solve for x, y, z, a, b

$$a = \frac{41}{4} = 10\frac{1}{4} = 10.25$$

$$b=\frac{1}{4}=0.25$$

Solution Steps

Consider the first equation. Divide both sides by 20.

$$x=\frac{5}{20}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{1}{4}$$

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

$$y=10+\frac{1}{4}$$

Add 10 and \frac{1}{4} to get \frac{41}{4}.

$$y=\frac{41}{4}$$

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

$$z=\frac{1}{4}$$

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

$$a=\frac{41}{4}$$

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

$$b=\frac{1}{4}$$

The system is now solved.

$$x=\frac{1}{4} y=\frac{41}{4} z=\frac{1}{4} a=\frac{41}{4} b=\frac{1}{4}$$