Solve {l}{4m-12=m-4}{4n+24=n+3}

$$\left. \begin{array} { l } { 4 m - 12 = m - 4 } \\ { 4 n + 24 = n + 3 } \end{array} \right.$$

Solve for m, n

$$m = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

$$n=-7$$

Solution Steps

Consider the first equation. Subtract m from both sides.

$$4m-12-m=-4$$

Combine 4m and -m to get 3m.

$$3m-12=-4$$

Add 12 to both sides.

$$3m=-4+12$$

Add -4 and 12 to get 8.

$$3m=8$$

Divide both sides by 3.

$$m=\frac{8}{3}$$

Consider the second equation. Subtract n from both sides.

$$4n+24-n=3$$

Combine 4n and -n to get 3n.

$$3n+24=3$$

Subtract 24 from both sides.

$$3n=3-24$$

Subtract 24 from 3 to get -21.

$$3n=-21$$

Divide both sides by 3.

$$n=\frac{-21}{3}$$

Divide -21 by 3 to get -7.

$$n=-7$$

The system is now solved.

$$m=\frac{8}{3} n=-7$$