Solve {l}{y=23}{4x-y=19}{z={(y/x-2)}}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = 23 }\\ { 4 x - y = 19 }\\ { z = {(\frac{y}{x} - 2)} }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a=\frac{4}{21}\approx 0.19047619$$

Solution Steps

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

$$4x-23=19$$

Add 23 to both sides.

$$4x=19+23$$

Add 19 and 23 to get 42.

$$4x=42$$

Divide both sides by 4.

$$x=\frac{42}{4}$$

Reduce the fraction \frac{42}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{21}{2}$$

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

$$z=\frac{23}{\frac{21}{2}}-2$$

Divide 23 by \frac{21}{2} by multiplying 23 by the reciprocal of \frac{21}{2}.

$$z=23\times \frac{2}{21}-2$$

Multiply 23 and \frac{2}{21} to get \frac{46}{21}.

$$z=\frac{46}{21}-2$$

Subtract 2 from \frac{46}{21} to get \frac{4}{21}.

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

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

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

The system is now solved.

$$y=23 x=\frac{21}{2} z=\frac{4}{21} a=\frac{4}{21}$$