Solve {l}{-7{(-37-5y)}-2y=y+3}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { -7 {(-37 - 5 y)} - 2 y = y + 3 }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for y, z, a, b

$$b=-8$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -7 by -37-5y.

$$259+35y-2y=y+3$$

Combine 35y and -2y to get 33y.

$$259+33y=y+3$$

Subtract y from both sides.

$$259+33y-y=3$$

Combine 33y and -y to get 32y.

$$259+32y=3$$

Subtract 259 from both sides.

$$32y=3-259$$

Subtract 259 from 3 to get -256.

$$32y=-256$$

Divide both sides by 32.

$$y=\frac{-256}{32}$$

Divide -256 by 32 to get -8.

$$y=-8$$

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

$$z=-8$$

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

$$a=-8$$

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

$$b=-8$$

The system is now solved.

$$y=-8 z=-8 a=-8 b=-8$$