Solve {l}{3-7x+2/8=2x+5x+1/9}{y=x+3x-1x+1}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 3 - \frac{7 x + 2}{8} = 2 x + \frac{5 x + 1}{9} }\\ { y = x + 3 x - 1 x + 1 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{43}{13} = 3\frac{4}{13} \approx 3.307692308$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 72, the least common multiple of 8,9.

$$216-9\left(7x+2\right)=144x+8\left(5x+1\right)$$

Use the distributive property to multiply -9 by 7x+2.

$$216-63x-18=144x+8\left(5x+1\right)$$

Subtract 18 from 216 to get 198.

$$198-63x=144x+8\left(5x+1\right)$$

Use the distributive property to multiply 8 by 5x+1.

$$198-63x=144x+40x+8$$

Combine 144x and 40x to get 184x.

$$198-63x=184x+8$$

Subtract 184x from both sides.

$$198-63x-184x=8$$

Combine -63x and -184x to get -247x.

$$198-247x=8$$

Subtract 198 from both sides.

$$-247x=8-198$$

Subtract 198 from 8 to get -190.

$$-247x=-190$$

Divide both sides by -247.

$$x=\frac{-190}{-247}$$

Reduce the fraction \frac{-190}{-247} to lowest terms by extracting and canceling out -19.

$$x=\frac{10}{13}$$

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

$$y=\frac{10}{13}+3\times \frac{10}{13}-\frac{10}{13}+1$$

Multiply 3 and \frac{10}{13} to get \frac{30}{13}.

$$y=\frac{10}{13}+\frac{30}{13}-\frac{10}{13}+1$$

Add \frac{10}{13} and \frac{30}{13} to get \frac{40}{13}.

$$y=\frac{40}{13}-\frac{10}{13}+1$$

Subtract \frac{10}{13} from \frac{40}{13} to get \frac{30}{13}.

$$y=\frac{30}{13}+1$$

Add \frac{30}{13} and 1 to get \frac{43}{13}.

$$y=\frac{43}{13}$$

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

$$z=\frac{43}{13}$$

The system is now solved.

$$x=\frac{10}{13} y=\frac{43}{13} z=\frac{43}{13}$$