Solve by Substitution 2x+4y=22 , 2x-2y=-8

$2 x + 4 y = 22$ , $2 x - 2 y = - 8$

Step 1

Solve for $x$ in $2 x + 4 y = 22$ .

Subtract $4 y$ from both sides of the equation.

$2 x = 22 - 4 y$

$2 x - 2 y = - 8$

Divide each term in $2 x = 22 - 4 y$ by $2$ and simplify.

Divide each term in $2 x = 22 - 4 y$ by $2$ .

$\frac{2 x}{2} = \frac{22}{2} + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{22}{2} + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

Divide $x$ by $1$ .

$x = \frac{22}{2} + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

$x = \frac{22}{2} + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

$x = \frac{22}{2} + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

Simplify the right side.

Simplify each term.

Divide $22$ by $2$ .

$x = 11 + \frac{- 4 y}{2}$

$2 x - 2 y = - 8$

Cancel the common factor of $- 4$ and $2$ .

Factor $2$ out of $- 4 y$ .

$x = 11 + \frac{2 (- 2 y)}{2}$

$2 x - 2 y = - 8$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 11 + \frac{2 (- 2 y)}{2 (1)}$

$2 x - 2 y = - 8$

Cancel the common factor.

$x = 11 + \frac{2 (- 2 y)}{2 \cdot 1}$

$2 x - 2 y = - 8$

Rewrite the expression.

$x = 11 + \frac{- 2 y}{1}$

$2 x - 2 y = - 8$

Divide $- 2 y$ by $1$ .

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

$x = 11 - 2 y$

$2 x - 2 y = - 8$

Step 2

Replace all occurrences of $x$ with $11 - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 2 y = - 8$ with $11 - 2 y$ .

$2 (11 - 2 y) - 2 y = - 8$

$x = 11 - 2 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 \cdot 11 + 2 (- 2 y) - 2 y = - 8$

$x = 11 - 2 y$

Multiply $2$ by $11$ .

$22 + 2 (- 2 y) - 2 y = - 8$

$x = 11 - 2 y$

Multiply $- 2$ by $2$ .

$22 - 4 y - 2 y = - 8$

$x = 11 - 2 y$

$22 - 4 y - 2 y = - 8$

$x = 11 - 2 y$

Subtract $2 y$ from $- 4 y$ .

$22 - 6 y = - 8$

$x = 11 - 2 y$

$22 - 6 y = - 8$

$x = 11 - 2 y$

$22 - 6 y = - 8$

$x = 11 - 2 y$

$22 - 6 y = - 8$

$x = 11 - 2 y$

Step 3

Solve for $y$ in $22 - 6 y = - 8$ .

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

Subtract $22$ from both sides of the equation.

$- 6 y = - 8 - 22$

$x = 11 - 2 y$

Subtract $22$ from $- 8$ .

$- 6 y = - 30$

$x = 11 - 2 y$

$- 6 y = - 30$

$x = 11 - 2 y$

Divide each term in $- 6 y = - 30$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 30$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 30}{- 6}$

$x = 11 - 2 y$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 30}{- 6}$

$x = 11 - 2 y$

Divide $y$ by $1$ .

$y = \frac{- 30}{- 6}$

$x = 11 - 2 y$

$y = \frac{- 30}{- 6}$

$x = 11 - 2 y$

$y = \frac{- 30}{- 6}$

$x = 11 - 2 y$

Simplify the right side.

Divide $- 30$ by $- 6$ .

$y = 5$

$x = 11 - 2 y$

$y = 5$

$x = 11 - 2 y$

$y = 5$

$x = 11 - 2 y$

$y = 5$

$x = 11 - 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = 11 - 2 y$ with $5$ .

$x = 11 - 2 \cdot 5$

$y = 5$

Simplify the right side.

Simplify $11 - 2 \cdot 5$ .

Multiply $- 2$ by $5$ .

$x = 11 - 10$

$y = 5$

Subtract $10$ from $11$ .

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

Step 5

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

$(1, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 5)$

Equation Form:

$x = 1, y = 5$

Step 7

Solve by Substitution 2x+4y=22 , 2x-2y=-8

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