Solve {l}{0=1+m+n}{4=9-3m+1}

$$\left. \begin{array} { l } { 0 = 1 + m + n } \\ { 4 = 9 - 3 m + 1 } \end{array} \right.$$

Solve for m, n

$$m=2$$

$$n=-3$$

Solution Steps

Consider the second equation. Add 9 and 1 to get 10.

$$4=10-3m$$

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

$$10-3m=4$$

Subtract 10 from both sides.

$$-3m=4-10$$

Subtract 10 from 4 to get -6.

$$-3m=-6$$

Divide both sides by -3.

$$m=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$m=2$$

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

$$0=1+2+n$$

Add 1 and 2 to get 3.

$$0=3+n$$

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

$$3+n=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$n=-3$$

The system is now solved.

$$m=2 n=-3$$