Solve by Substitution x+y=12 , x-y=2

$x + y = 12$ , $x - y = 2$

Step 1

Subtract $y$ from both sides of the equation.

$x = 12 - y$

$x - y = 2$

Step 2

Replace all occurrences of $x$ with $12 - y$ in each equation.

Replace all occurrences of $x$ in $x - y = 2$ with $12 - y$ .

$(12 - y) - y = 2$

$x = 12 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$12 - 2 y = 2$

$x = 12 - y$

$12 - 2 y = 2$

$x = 12 - y$

$12 - 2 y = 2$

$x = 12 - y$

Step 3

Solve for $y$ in $12 - 2 y = 2$ .

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

Subtract $12$ from both sides of the equation.

$- 2 y = 2 - 12$

$x = 12 - y$

Subtract $12$ from $2$ .

$- 2 y = - 10$

$x = 12 - y$

$- 2 y = - 10$

$x = 12 - y$

Divide each term in $- 2 y = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 10$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 10}{- 2}$

$x = 12 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 10}{- 2}$

$x = 12 - y$

Divide $y$ by $1$ .

$y = \frac{- 10}{- 2}$

$x = 12 - y$

$y = \frac{- 10}{- 2}$

$x = 12 - y$

$y = \frac{- 10}{- 2}$

$x = 12 - y$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$y = 5$

$x = 12 - y$

$y = 5$

$x = 12 - y$

$y = 5$

$x = 12 - y$

$y = 5$

$x = 12 - y$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = 12 - y$ with $5$ .

$x = 12 - (5)$

$y = 5$

Simplify the right side.

Simplify $12 - (5)$ .

Multiply $- 1$ by $5$ .

$x = 12 - 5$

$y = 5$

Subtract $5$ from $12$ .

$x = 7$

$y = 5$

$x = 7$

$y = 5$

$x = 7$

$y = 5$

$x = 7$

$y = 5$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(7, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, 5)$

Equation Form:

$x = 7, y = 5$

Step 7

Solve by Substitution x+y=12 , x-y=2

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