Solve the System of Equations -m+n=9 m+n=5

$- m + n = 9$ $m + n = 5$

Step 1

Add $m$ to both sides of the equation.

$n = 9 + m$

$m + n = 5$

Step 2

Replace all occurrences of $n$ with $9 + m$ in each equation.

Replace all occurrences of $n$ in $m + n = 5$ with $9 + m$ .

$m + 9 + m = 5$

$n = 9 + m$

Simplify the left side.

Simplify $m + 9 + m$ .

Remove parentheses.

$m + 9 + m = 5$

$n = 9 + m$

Add $m$ and $m$ .

$2 m + 9 = 5$

$n = 9 + m$

$2 m + 9 = 5$

$n = 9 + m$

$2 m + 9 = 5$

$n = 9 + m$

$2 m + 9 = 5$

$n = 9 + m$

Step 3

Solve for $m$ in $2 m + 9 = 5$ .

Move all terms not containing $m$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$2 m = 5 - 9$

$n = 9 + m$

Subtract $9$ from $5$ .

$2 m = - 4$

$n = 9 + m$

$2 m = - 4$

$n = 9 + m$

Divide each term in $2 m = - 4$ by $2$ and simplify.

Divide each term in $2 m = - 4$ by $2$ .

$\frac{2 m}{2} = \frac{- 4}{2}$

$n = 9 + m$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{- 4}{2}$

$n = 9 + m$

Divide $m$ by $1$ .

$m = \frac{- 4}{2}$

$n = 9 + m$

$m = \frac{- 4}{2}$

$n = 9 + m$

$m = \frac{- 4}{2}$

$n = 9 + m$

Simplify the right side.

Divide $- 4$ by $2$ .

$m = - 2$

$n = 9 + m$

$m = - 2$

$n = 9 + m$

$m = - 2$

$n = 9 + m$

$m = - 2$

$n = 9 + m$

Step 4

Replace all occurrences of $m$ with $- 2$ in each equation.

Replace all occurrences of $m$ in $n = 9 + m$ with $- 2$ .

$n = 9 - 2$

$m = - 2$

Simplify $n = 9 - 2$ .

Simplify the left side.

Remove parentheses.

$n = 9 - 2$

$m = - 2$

$n = 9 - 2$

$m = - 2$

Simplify the right side.

Subtract $2$ from $9$ .

$n = 7$

$m = - 2$

$n = 7$

$m = - 2$

$n = 7$

$m = - 2$

$n = 7$

$m = - 2$

Step 5

List all of the solutions.

$n = 7, m = - 2$

Solve the System of Equations -m+n=9 m+n=5

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