Solve by Substitution x+y=9 , x-y=-1

$x + y = 9$ , $x - y = - 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = 9 - y$

$x - y = - 1$

Step 2

Replace all occurrences of $x$ with $9 - y$ in each equation.

Replace all occurrences of $x$ in $x - y = - 1$ with $9 - y$ .

$(9 - y) - y = - 1$

$x = 9 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$9 - 2 y = - 1$

$x = 9 - y$

$9 - 2 y = - 1$

$x = 9 - y$

$9 - 2 y = - 1$

$x = 9 - y$

Step 3

Solve for $y$ in $9 - 2 y = - 1$ .

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

Subtract $9$ from both sides of the equation.

$- 2 y = - 1 - 9$

$x = 9 - y$

Subtract $9$ from $- 1$ .

$- 2 y = - 10$

$x = 9 - y$

$- 2 y = - 10$

$x = 9 - y$

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

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

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

$x = 9 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x = 9 - y$

Divide $y$ by $1$ .

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

$x = 9 - y$

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

$x = 9 - y$

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

$x = 9 - y$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$y = 5$

$x = 9 - y$

$y = 5$

$x = 9 - y$

$y = 5$

$x = 9 - y$

$y = 5$

$x = 9 - y$

Step 4

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

Replace all occurrences of $y$ in $x = 9 - y$ with $5$ .

$x = 9 - (5)$

$y = 5$

Simplify the right side.

Simplify $9 - (5)$ .

Multiply $- 1$ by $5$ .

$x = 9 - 5$

$y = 5$

Subtract $5$ from $9$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 5

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

$(4, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 5)$

Equation Form:

$x = 4, y = 5$

Step 7

Solve by Substitution x+y=9 , x-y=-1

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