Solve {l}{4x=3}{y={(x-2)}{(x+2)}-x{(x-1)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 4 x = 3 }\\ { y = {(x - 2)} {(x + 2)} - x {(x - 1)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

Solution Steps

Consider the first equation. Divide both sides by 4.

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

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

$$y=\left(\frac{3}{4}-2\right)\left(\frac{3}{4}+2\right)-\frac{3}{4}\left(\frac{3}{4}-1\right)$$

Subtract 2 from \frac{3}{4} to get -\frac{5}{4}.

$$y=-\frac{5}{4}\left(\frac{3}{4}+2\right)-\frac{3}{4}\left(\frac{3}{4}-1\right)$$

Add \frac{3}{4} and 2 to get \frac{11}{4}.

$$y=-\frac{5}{4}\times \frac{11}{4}-\frac{3}{4}\left(\frac{3}{4}-1\right)$$

Multiply -\frac{5}{4} and \frac{11}{4} to get -\frac{55}{16}.

$$y=-\frac{55}{16}-\frac{3}{4}\left(\frac{3}{4}-1\right)$$

Subtract 1 from \frac{3}{4} to get -\frac{1}{4}.

$$y=-\frac{55}{16}-\frac{3}{4}\left(-\frac{1}{4}\right)$$

Multiply \frac{3}{4} and -\frac{1}{4} to get -\frac{3}{16}.

$$y=-\frac{55}{16}-\left(-\frac{3}{16}\right)$$

The opposite of -\frac{3}{16} is \frac{3}{16}.

$$y=-\frac{55}{16}+\frac{3}{16}$$

Add -\frac{55}{16} and \frac{3}{16} to get -\frac{13}{4}.

$$y=-\frac{13}{4}$$

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

$$z=-\frac{13}{4}$$

The system is now solved.

$$x=\frac{3}{4} y=-\frac{13}{4} z=-\frac{13}{4}$$