Solve by Substitution -2x-y=-9 , 5x-2y=18

$- 2 x - y = - 9$ , $5 x - 2 y = 18$

Solve for $y$ in the first equation.

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

$- y = - 9 + 2 x$

$5 x - 2 y = 18$

Multiply each term in $- y = - 9 + 2 x$ by $- 1$

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Multiply each term in $- y = - 9 + 2 x$ by $- 1$ .

$(- y) \cdot - 1 = (- 9) \cdot - 1 + 2 x \cdot - 1$

$5 x - 2 y = 18$

Multiply $(- y) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 y = (- 9) \cdot - 1 + 2 x \cdot - 1$

$5 x - 2 y = 18$

Multiply $y$ by $1$ .

$y = (- 9) \cdot - 1 + 2 x \cdot - 1$

$5 x - 2 y = 18$

$y = (- 9) \cdot - 1 + 2 x \cdot - 1$

$5 x - 2 y = 18$

Simplify each term.

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Multiply $- 9$ by $- 1$ .

$y = 9 + 2 x \cdot - 1$

$5 x - 2 y = 18$

Multiply $- 1$ by $2$ .

$y = 9 - 2 x$

$5 x - 2 y = 18$

$y = 9 - 2 x$

$5 x - 2 y = 18$

$y = 9 - 2 x$

$5 x - 2 y = 18$

$y = 9 - 2 x$

$5 x - 2 y = 18$

Replace all occurrences of $y$ with $9 - 2 x$ in each equation.

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Replace all occurrences of $y$ in $5 x - 2 y = 18$ with $9 - 2 x$ .

$5 x - 2 (9 - 2 x) = 18$

$y = 9 - 2 x$

Simplify $5 x - 2 (9 - 2 x)$ .

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Simplify each term.

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Apply the distributive property.

$5 x - 2 \cdot 9 - 2 (- 2 x) = 18$

$y = 9 - 2 x$

Multiply $- 2$ by $9$ .

$5 x - 18 - 2 (- 2 x) = 18$

$y = 9 - 2 x$

Multiply $- 2$ by $- 2$ .

$5 x - 18 + 4 x = 18$

$y = 9 - 2 x$

$5 x - 18 + 4 x = 18$

$y = 9 - 2 x$

Add $5 x$ and $4 x$ .

$9 x - 18 = 18$

$y = 9 - 2 x$

$9 x - 18 = 18$

$y = 9 - 2 x$

$9 x - 18 = 18$

$y = 9 - 2 x$

Solve for $x$ in the first equation.

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

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Add $18$ to both sides of the equation.

$9 x = 18 + 18$

$y = 9 - 2 x$

Add $18$ and $18$ .

$9 x = 36$

$y = 9 - 2 x$

$9 x = 36$

$y = 9 - 2 x$

Divide each term by $9$ and simplify.

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Divide each term in $9 x = 36$ by $9$ .

$\frac{9 x}{9} = \frac{36}{9}$

$y = 9 - 2 x$

Cancel the common factor of $9$ .

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Cancel the common factor.

$\frac{9 x}{9} = \frac{36}{9}$

$y = 9 - 2 x$

Divide $x$ by $1$ .

$x = \frac{36}{9}$

$y = 9 - 2 x$

$x = \frac{36}{9}$

$y = 9 - 2 x$

Divide $36$ by $9$ .

$x = 4$

$y = 9 - 2 x$

$x = 4$

$y = 9 - 2 x$

$x = 4$

$y = 9 - 2 x$

Replace all occurrences of $x$ with $4$ in each equation.

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Replace all occurrences of $x$ in $y = 9 - 2 x$ with $4$ .

$y = 9 - 2 \cdot 4$

$x = 4$

Simplify $9 - 2 \cdot 4$ .

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Multiply $- 2$ by $4$ .

$y = 9 - 8$

$x = 4$

Subtract $8$ from $9$ .

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

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

$(4, 1)$

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Solve by Substitution -2x-y=-9 , 5x-2y=18

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