Solve {l}{2m+m=7}{2n+m=2}

$$\left\{ \begin{array} { l } { 2 m + m = 7 } \\ { 2 n + m = 2 } \end{array} \right.$$

Solve for m, n

$$m = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$n=-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Consider the first equation. Combine 2m and m to get 3m.

$$3m=7$$

Divide both sides by 3.

$$m=\frac{7}{3}$$

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

$$2n+\frac{7}{3}=2$$

Subtract \frac{7}{3} from both sides.

$$2n=2-\frac{7}{3}$$

Subtract \frac{7}{3} from 2 to get -\frac{1}{3}.

$$2n=-\frac{1}{3}$$

Divide both sides by 2.

$$n=\frac{-\frac{1}{3}}{2}$$

Express \frac{-\frac{1}{3}}{2} as a single fraction.

$$n=\frac{-1}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$n=\frac{-1}{6}$$

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$n=-\frac{1}{6}$$

The system is now solved.

$$m=\frac{7}{3} n=-\frac{1}{6}$$