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

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

Add $2 y$ to both sides of the equation.

$x = 11 + 2 y$

$2 x + y = 2$

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

$x = 11 + 2 y$

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

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

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Simplify each term.

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Apply the distributive property.

$x = 11 + 2 y$

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

Multiply $2$ by $11$ .

$x = 11 + 2 y$

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

Multiply $2$ by $2$ .

$x = 11 + 2 y$

$22 + 4 y + y = 2$

$x = 11 + 2 y$

$22 + 4 y + y = 2$

Add $4 y$ and $y$ .

$x = 11 + 2 y$

$22 + 5 y = 2$

$x = 11 + 2 y$

$22 + 5 y = 2$

Solve for $y$ in the second equation.

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

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Subtract $22$ from both sides of the equation.

$x = 11 + 2 y$

$5 y = 2 - 22$

Subtract $22$ from $2$ .

$x = 11 + 2 y$

$5 y = - 20$

$x = 11 + 2 y$

$5 y = - 20$

Divide each term by $5$ and simplify.

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Divide each term in $5 y = - 20$ by $5$ .

$x = 11 + 2 y$

$\frac{5 y}{5} = \frac{- 20}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$x = 11 + 2 y$

$\frac{5 y}{5} = \frac{- 20}{5}$

Divide $y$ by $1$ .

$x = 11 + 2 y$

$y = \frac{- 20}{5}$

$x = 11 + 2 y$

$y = \frac{- 20}{5}$

Divide $- 20$ by $5$ .

$x = 11 + 2 y$

$y = - 4$

$x = 11 + 2 y$

$y = - 4$

$x = 11 + 2 y$

$y = - 4$

Replace all occurrences of $y$ in $x = 11 + 2 y$ with $- 4$ .

$x = 11 + 2 (- 4)$

$y = - 4$

Simplify $11 + 2 (- 4)$ .

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Multiply $2$ by $- 4$ .

$x = 11 - 8$

$y = - 4$

Subtract $8$ from $11$ .

$x = 3$

$y = - 4$

$x = 3$

$y = - 4$

The solution to the system of equations can be represented as a point.

$(3, - 4)$

The result can be shown in multiple forms.

Point Form:

$(3, - 4)$

Equation Form:

$x = 3, y = - 4$

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

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