Solve by Substitution 2m=n+3 n-3m=-8

$2 m = n + 3$ $n - 3 m = - 8$

Step 1

Divide each term in $2 m = n + 3$ by $2$ and simplify.

Divide each term in $2 m = n + 3$ by $2$ .

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

$n - 3 m = - 8$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$n - 3 m = - 8$

Divide $m$ by $1$ .

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

$n - 3 m = - 8$

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

$n - 3 m = - 8$

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

$n - 3 m = - 8$

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

$n - 3 m = - 8$

Step 2

Replace all occurrences of $m$ with $\frac{n}{2} + \frac{3}{2}$ in each equation.

Replace all occurrences of $m$ in $n - 3 m = - 8$ with $\frac{n}{2} + \frac{3}{2}$ .

$n - 3 (\frac{n}{2} + \frac{3}{2}) = - 8$

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

Simplify the left side.

Simplify $n - 3 (\frac{n}{2} + \frac{3}{2})$ .

Simplify each term.

Apply the distributive property.

$n - 3 \frac{n}{2} - 3 (\frac{3}{2}) = - 8$

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

Combine $- 3$ and $\frac{n}{2}$ .

$n + \frac{- 3 n}{2} - 3 (\frac{3}{2}) = - 8$

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

Multiply $- 3 (\frac{3}{2})$ .

Combine $- 3$ and $\frac{3}{2}$ .

$n + \frac{- 3 n}{2} + \frac{- 3 \cdot 3}{2} = - 8$

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

Multiply $- 3$ by $3$ .

$n + \frac{- 3 n}{2} + \frac{- 9}{2} = - 8$

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

$n + \frac{- 3 n}{2} + \frac{- 9}{2} = - 8$

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

Simplify each term.

Move the negative in front of the fraction.

$n - \frac{(3) n}{2} + \frac{- 9}{2} = - 8$

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

Move the negative in front of the fraction.

$n - \frac{3 n}{2} - \frac{9}{2} = - 8$

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

$n - \frac{3 n}{2} - \frac{9}{2} = - 8$

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

$n - \frac{3 n}{2} - \frac{9}{2} = - 8$

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

To write $n$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$n \cdot \frac{2}{2} - \frac{3 n}{2} - \frac{9}{2} = - 8$

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

Simplify terms.

Combine $n$ and $\frac{2}{2}$ .

$\frac{n \cdot 2}{2} - \frac{3 n}{2} - \frac{9}{2} = - 8$

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

Combine the numerators over the common denominator.

$\frac{n \cdot 2 - 3 n}{2} - \frac{9}{2} = - 8$

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

Combine the numerators over the common denominator.

$\frac{n \cdot 2 - 3 n - 9}{2} = - 8$

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

$\frac{n \cdot 2 - 3 n - 9}{2} = - 8$

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

Move $2$ to the left of $n$ .

$\frac{2 n - 3 n - 9}{2} = - 8$

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

Simplify terms.

Subtract $3 n$ from $2 n$ .

$\frac{- n - 9}{2} = - 8$

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

Factor $- 1$ out of $- n$ .

$\frac{- (n) - 9}{2} = - 8$

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

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- (n) - 1 \cdot 9}{2} = - 8$

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

Factor $- 1$ out of $- (n) - 1 (9)$ .

$\frac{- (n + 9)}{2} = - 8$

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

Simplify the expression.

Rewrite $- (n + 9)$ as $- 1 (n + 9)$ .

$\frac{- 1 (n + 9)}{2} = - 8$

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

Move the negative in front of the fraction.

$- \frac{n + 9}{2} = - 8$

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

$- \frac{n + 9}{2} = - 8$

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

$- \frac{n + 9}{2} = - 8$

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

$- \frac{n + 9}{2} = - 8$

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

$- \frac{n + 9}{2} = - 8$

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

$- \frac{n + 9}{2} = - 8$

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

Step 3

Solve for $n$ in $- \frac{n + 9}{2} = - 8$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{n + 9}{2}) = - 2 \cdot - 8$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{n + 9}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{n + 9}{2}$ into the numerator.

$- 2 \frac{- (n + 9)}{2} = - 2 \cdot - 8$

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

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (n + 9)}{2}) = - 2 \cdot - 8$

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

Cancel the common factor.

$2 \cdot (- 1 \frac{- (n + 9)}{2}) = - 2 \cdot - 8$

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

Rewrite the expression.

$n + 9 = - 2 \cdot - 8$

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

$n + 9 = - 2 \cdot - 8$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (n + 9) = - 2 \cdot - 8$

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

Multiply $n + 9$ by $1$ .

$n + 9 = - 2 \cdot - 8$

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

$n + 9 = - 2 \cdot - 8$

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

$n + 9 = - 2 \cdot - 8$

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

$n + 9 = - 2 \cdot - 8$

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

Simplify the right side.

Multiply $- 2$ by $- 8$ .

$n + 9 = 16$

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

$n + 9 = 16$

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

$n + 9 = 16$

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

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

Subtract $9$ from both sides of the equation.

$n = 16 - 9$

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

Subtract $9$ from $16$ .

$n = 7$

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

$n = 7$

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

$n = 7$

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

Step 4

Replace all occurrences of $n$ with $7$ in each equation.

Replace all occurrences of $n$ in $m = \frac{n}{2} + \frac{3}{2}$ with $7$ .

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

$n = 7$

Simplify the right side.

Simplify $\frac{7}{2} + \frac{3}{2}$ .

Combine the numerators over the common denominator.

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

$n = 7$

Simplify the expression.

Add $7$ and $3$ .

$m = \frac{10}{2}$

$n = 7$

Divide $10$ by $2$ .

$m = 5$

$n = 7$

$m = 5$

$n = 7$

$m = 5$

$n = 7$

$m = 5$

$n = 7$

$m = 5$

$n = 7$

Step 5

List all of the solutions.

$m = 5, n = 7$

Solve by Substitution 2m=n+3 n-3m=-8

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