Solve {l}{23x-16=14-17x}{y=x{(x+4)}+x{(x+2)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 23 x - 16 = 14 - 17 x }\\ { y = x {(x + 4)} + x {(x + 2)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{45}{8} = 5\frac{5}{8} = 5.625$$

Solution Steps

Consider the first equation. Add 17x to both sides.

$$23x-16+17x=14$$

Combine 23x and 17x to get 40x.

$$40x-16=14$$

Add 16 to both sides.

$$40x=14+16$$

Add 14 and 16 to get 30.

$$40x=30$$

Divide both sides by 40.

$$x=\frac{30}{40}$$

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

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

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

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

Add \frac{3}{4} and 4 to get \frac{19}{4}.

$$y=\frac{3}{4}\times \frac{19}{4}+\frac{3}{4}\left(\frac{3}{4}+2\right)$$

Multiply \frac{3}{4} and \frac{19}{4} to get \frac{57}{16}.

$$y=\frac{57}{16}+\frac{3}{4}\left(\frac{3}{4}+2\right)$$

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

$$y=\frac{57}{16}+\frac{3}{4}\times \frac{11}{4}$$

Multiply \frac{3}{4} and \frac{11}{4} to get \frac{33}{16}.

$$y=\frac{57}{16}+\frac{33}{16}$$

Add \frac{57}{16} and \frac{33}{16} to get \frac{45}{8}.

$$y=\frac{45}{8}$$

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

$$z=\frac{45}{8}$$

The system is now solved.

$$x=\frac{3}{4} y=\frac{45}{8} z=\frac{45}{8}$$