Solve {l}{m+n/2-m-2n/4=2}{m+n/2+m-2n/4=0}

$$\left\{ \begin{array} { l } { \frac { m + n } { 2 } - \frac { m - 2 n } { 4 } = 2 } \\ { \frac { m + n } { 2 } + \frac { m - 2 n } { 4 } = 0 } \end{array} \right.$$

Solve for m, n

$$m=0$$

$$n=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(m+n\right)-\left(m-2n\right)=8$$

Use the distributive property to multiply 2 by m+n.

$$2m+2n-\left(m-2n\right)=8$$

To find the opposite of m-2n, find the opposite of each term.

$$2m+2n-m+2n=8$$

Combine 2m and -m to get m.

$$m+2n+2n=8$$

Combine 2n and 2n to get 4n.

$$m+4n=8$$

Consider the second equation. Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(m+n\right)+m-2n=0$$

Use the distributive property to multiply 2 by m+n.

$$2m+2n+m-2n=0$$

Combine 2m and m to get 3m.

$$3m+2n-2n=0$$

Combine 2n and -2n to get 0.

$$3m=0$$

Divide both sides by 3. Zero divided by any non-zero number gives zero.

$$m=0$$

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

$$0+4n=8$$

Anything plus zero gives itself.

$$4n=8$$

Divide both sides by 4.

$$n=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$n=2$$

The system is now solved.

$$m=0 n=2$$