Solve by Substitution x-y=11 , 2x+y=19

$x - y = 11$ , $2 x + y = 19$

Step 1

Add $y$ to both sides of the equation.

$x = 11 + y$

$2 x + y = 19$

Step 2

Replace all occurrences of $x$ with $11 + y$ in each equation.

Replace all occurrences of $x$ in $2 x + y = 19$ with $11 + y$ .

$2 (11 + y) + y = 19$

$x = 11 + y$

Simplify the left side.

Simplify $2 (11 + y) + y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 11 + 2 y + y = 19$

$x = 11 + y$

Multiply $2$ by $11$ .

$22 + 2 y + y = 19$

$x = 11 + y$

$22 + 2 y + y = 19$

$x = 11 + y$

Add $2 y$ and $y$ .

$22 + 3 y = 19$

$x = 11 + y$

$22 + 3 y = 19$

$x = 11 + y$

$22 + 3 y = 19$

$x = 11 + y$

$22 + 3 y = 19$

$x = 11 + y$

Step 3

Solve for $y$ in $22 + 3 y = 19$ .

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

Subtract $22$ from both sides of the equation.

$3 y = 19 - 22$

$x = 11 + y$

Subtract $22$ from $19$ .

$3 y = - 3$

$x = 11 + y$

$3 y = - 3$

$x = 11 + y$

Divide each term in $3 y = - 3$ by $3$ and simplify.

Divide each term in $3 y = - 3$ by $3$ .

$\frac{3 y}{3} = \frac{- 3}{3}$

$x = 11 + y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 3}{3}$

$x = 11 + y$

Divide $y$ by $1$ .

$y = \frac{- 3}{3}$

$x = 11 + y$

$y = \frac{- 3}{3}$

$x = 11 + y$

$y = \frac{- 3}{3}$

$x = 11 + y$

Simplify the right side.

Divide $- 3$ by $3$ .

$y = - 1$

$x = 11 + y$

$y = - 1$

$x = 11 + y$

$y = - 1$

$x = 11 + y$

$y = - 1$

$x = 11 + y$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = 11 + y$ with $- 1$ .

$x = 11 - 1$

$y = - 1$

Simplify $x = 11 - 1$ .

Simplify the left side.

Remove parentheses.

$x = 11 - 1$

$y = - 1$

$x = 11 - 1$

$y = - 1$

Simplify the right side.

Subtract $1$ from $11$ .

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

Step 5

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

$(10, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(10, - 1)$

Equation Form:

$x = 10, y = - 1$

Step 7

Solve by Substitution x-y=11 , 2x+y=19

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