Solve {l}{5x+2/6-8x-1/3=4x+2/5-5}{y=5{(5x+2)}-10{(8x-1)}-6{(4x+2)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{5 x + 2}{6} - \frac{8 x - 1}{3} = \frac{4 x + 2}{5} - 5 }\\ { y = 5 {(5 x + 2)} - 10 {(8 x - 1)} - 6 {(4 x + 2)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-150$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 30, the least common multiple of 6,3,5.

$$5\left(5x+2\right)-10\left(8x-1\right)=6\left(4x+2\right)-150$$

Use the distributive property to multiply 5 by 5x+2.

$$25x+10-10\left(8x-1\right)=6\left(4x+2\right)-150$$

Use the distributive property to multiply -10 by 8x-1.

$$25x+10-80x+10=6\left(4x+2\right)-150$$

Combine 25x and -80x to get -55x.

$$-55x+10+10=6\left(4x+2\right)-150$$

Add 10 and 10 to get 20.

$$-55x+20=6\left(4x+2\right)-150$$

Use the distributive property to multiply 6 by 4x+2.

$$-55x+20=24x+12-150$$

Subtract 150 from 12 to get -138.

$$-55x+20=24x-138$$

Subtract 24x from both sides.

$$-55x+20-24x=-138$$

Combine -55x and -24x to get -79x.

$$-79x+20=-138$$

Subtract 20 from both sides.

$$-79x=-138-20$$

Subtract 20 from -138 to get -158.

$$-79x=-158$$

Divide both sides by -79.

$$x=\frac{-158}{-79}$$

Divide -158 by -79 to get 2.

$$x=2$$

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

$$y=5\left(5\times 2+2\right)-10\left(8\times 2-1\right)-6\left(4\times 2+2\right)$$

Multiply 5 and 2 to get 10.

$$y=5\left(10+2\right)-10\left(8\times 2-1\right)-6\left(4\times 2+2\right)$$

Add 10 and 2 to get 12.

$$y=5\times 12-10\left(8\times 2-1\right)-6\left(4\times 2+2\right)$$

Multiply 5 and 12 to get 60.

$$y=60-10\left(8\times 2-1\right)-6\left(4\times 2+2\right)$$

Multiply 8 and 2 to get 16.

$$y=60-10\left(16-1\right)-6\left(4\times 2+2\right)$$

Subtract 1 from 16 to get 15.

$$y=60-10\times 15-6\left(4\times 2+2\right)$$

Multiply -10 and 15 to get -150.

$$y=60-150-6\left(4\times 2+2\right)$$

Subtract 150 from 60 to get -90.

$$y=-90-6\left(4\times 2+2\right)$$

Multiply 4 and 2 to get 8.

$$y=-90-6\left(8+2\right)$$

Add 8 and 2 to get 10.

$$y=-90-6\times 10$$

Multiply -6 and 10 to get -60.

$$y=-90-60$$

Subtract 60 from -90 to get -150.

$$y=-150$$

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

$$z=-150$$

The system is now solved.

$$x=2 y=-150 z=-150$$