Solve by Substitution -v+w=7 v+w=1

$- v + w = 7$ $v + w = 1$

Step 1

Add $v$ to both sides of the equation.

$w = 7 + v$

$v + w = 1$

Step 2

Replace all occurrences of $w$ with $7 + v$ in each equation.

Replace all occurrences of $w$ in $v + w = 1$ with $7 + v$ .

$v + 7 + v = 1$

$w = 7 + v$

Simplify the left side.

Simplify $v + 7 + v$ .

Remove parentheses.

$v + 7 + v = 1$

$w = 7 + v$

Add $v$ and $v$ .

$2 v + 7 = 1$

$w = 7 + v$

$2 v + 7 = 1$

$w = 7 + v$

$2 v + 7 = 1$

$w = 7 + v$

$2 v + 7 = 1$

$w = 7 + v$

Step 3

Solve for $v$ in $2 v + 7 = 1$ .

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

Subtract $7$ from both sides of the equation.

$2 v = 1 - 7$

$w = 7 + v$

Subtract $7$ from $1$ .

$2 v = - 6$

$w = 7 + v$

$2 v = - 6$

$w = 7 + v$

Divide each term in $2 v = - 6$ by $2$ and simplify.

Divide each term in $2 v = - 6$ by $2$ .

$\frac{2 v}{2} = \frac{- 6}{2}$

$w = 7 + v$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 v}{2} = \frac{- 6}{2}$

$w = 7 + v$

Divide $v$ by $1$ .

$v = \frac{- 6}{2}$

$w = 7 + v$

$v = \frac{- 6}{2}$

$w = 7 + v$

$v = \frac{- 6}{2}$

$w = 7 + v$

Simplify the right side.

Divide $- 6$ by $2$ .

$v = - 3$

$w = 7 + v$

$v = - 3$

$w = 7 + v$

$v = - 3$

$w = 7 + v$

$v = - 3$

$w = 7 + v$

Step 4

Replace all occurrences of $v$ with $- 3$ in each equation.

Replace all occurrences of $v$ in $w = 7 + v$ with $- 3$ .

$w = 7 - 3$

$v = - 3$

Simplify $w = 7 - 3$ .

Simplify the left side.

Remove parentheses.

$w = 7 - 3$

$v = - 3$

$w = 7 - 3$

$v = - 3$

Simplify the right side.

Subtract $3$ from $7$ .

$w = 4$

$v = - 3$

$w = 4$

$v = - 3$

$w = 4$

$v = - 3$

$w = 4$

$v = - 3$

Step 5

List all of the solutions.

$w = 4, v = - 3$

Solve by Substitution -v+w=7 v+w=1

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