Solve {l}{82=2(-5m+1)}{-2(1+8r)=94}

$$\left. \begin{array} { l } { 82 = 2 ( - 5 m + 1 ) } \\ { - 2 ( 1 + 8 r ) = 94 } \end{array} \right.$$

Solve for m, r

$$r=-6$$

$$m=-8$$

Solution Steps

Consider the first equation. Divide both sides by 2.

$$\frac{82}{2}=-5m+1$$

Divide 82 by 2 to get 41.

$$41=-5m+1$$

Swap sides so that all variable terms are on the left hand side.

$$-5m+1=41$$

Subtract 1 from both sides.

$$-5m=41-1$$

Subtract 1 from 41 to get 40.

$$-5m=40$$

Divide both sides by -5.

$$m=\frac{40}{-5}$$

Divide 40 by -5 to get -8.

$$m=-8$$

Consider the second equation. Divide both sides by -2.

$$1+8r=\frac{94}{-2}$$

Divide 94 by -2 to get -47.

$$1+8r=-47$$

Subtract 1 from both sides.

$$8r=-47-1$$

Subtract 1 from -47 to get -48.

$$8r=-48$$

Divide both sides by 8.

$$r=\frac{-48}{8}$$

Divide -48 by 8 to get -6.

$$r=-6$$

The system is now solved.

$$m=-8 r=-6$$