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

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

Step 1

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

Add $y$ to both sides of the equation.

$- 2 x = - 9 + y$

$5 x - 2 y = 18$

Divide each term in $- 2 x = - 9 + y$ by $- 2$ and simplify.

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

$\frac{- 2 x}{- 2} = \frac{- 9}{- 2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 9}{- 2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

$x = \frac{- 9}{- 2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

$x = \frac{- 9}{- 2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{9}{2} + \frac{y}{- 2}$

$5 x - 2 y = 18$

Move the negative in front of the fraction.

$x = \frac{9}{2} - \frac{y}{2}$

$5 x - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$5 x - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$5 x - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$5 x - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$5 x - 2 y = 18$

Step 2

Replace all occurrences of $x$ with $\frac{9}{2} - \frac{y}{2}$ in each equation.

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

$5 (\frac{9}{2} - \frac{y}{2}) - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify the left side.

Simplify $5 (\frac{9}{2} - \frac{y}{2}) - 2 y$ .

Simplify each term.

Apply the distributive property.

$5 (\frac{9}{2}) + 5 (- \frac{y}{2}) - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Multiply $5 (\frac{9}{2})$ .

Combine $5$ and $\frac{9}{2}$ .

$\frac{5 \cdot 9}{2} + 5 (- \frac{y}{2}) - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Multiply $5$ by $9$ .

$\frac{45}{2} + 5 (- \frac{y}{2}) - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{45}{2} + 5 (- \frac{y}{2}) - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Multiply $5 (- \frac{y}{2})$ .

Multiply $- 1$ by $5$ .

$\frac{45}{2} - 5 \frac{y}{2} - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Combine $- 5$ and $\frac{y}{2}$ .

$\frac{45}{2} + \frac{- 5 y}{2} - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{45}{2} + \frac{- 5 y}{2} - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Move the negative in front of the fraction.

$\frac{45}{2} - \frac{5 y}{2} - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{45}{2} - \frac{5 y}{2} - 2 y = 18$

$x = \frac{9}{2} - \frac{y}{2}$

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{45}{2} - \frac{5 y}{2} - 2 y \cdot \frac{2}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Combine $- 2 y$ and $\frac{2}{2}$ .

$\frac{45}{2} - \frac{5 y}{2} + \frac{- 2 y \cdot 2}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$\frac{45}{2} + \frac{- 5 y - 2 y \cdot 2}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$\frac{45 - 5 y - 2 y \cdot 2}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Multiply $2$ by $- 2$ .

$\frac{45 - 5 y - 4 y}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Subtract $4 y$ from $- 5 y$ .

$\frac{45 - 9 y}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Factor $9$ out of $45 - 9 y$ .

Factor $9$ out of $45$ .

$\frac{9 (5) - 9 y}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Factor $9$ out of $- 9 y$ .

$\frac{9 (5) + 9 (- y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Factor $9$ out of $9 (5) + 9 (- y)$ .

$\frac{9 (5 - y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{9 (5 - y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{9 (5 - y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{9 (5 - y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

$\frac{9 (5 - y)}{2} = 18$

$x = \frac{9}{2} - \frac{y}{2}$

Step 3

Solve for $y$ in $\frac{9 (5 - y)}{2} = 18$ .

Multiply both sides by $2$ .

$\frac{9 (5 - y)}{2} \cdot 2 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify.

Simplify the left side.

Simplify $\frac{9 (5 - y)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 (5 - y)}{2} \cdot 2 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Rewrite the expression.

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

$x = \frac{9}{2} - \frac{y}{2}$

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

$x = \frac{9}{2} - \frac{y}{2}$

Apply the distributive property.

$9 \cdot 5 + 9 (- y) = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify the expression.

Multiply $9$ by $5$ .

$45 + 9 (- y) = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Multiply $- 1$ by $9$ .

$45 - 9 y = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Reorder $45$ and $- 9 y$ .

$- 9 y + 45 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y + 45 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y + 45 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y + 45 = 18 \cdot 2$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify the right side.

Multiply $18$ by $2$ .

$- 9 y + 45 = 36$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y + 45 = 36$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y + 45 = 36$

$x = \frac{9}{2} - \frac{y}{2}$

Solve for $y$ .

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

Subtract $45$ from both sides of the equation.

$- 9 y = 36 - 45$

$x = \frac{9}{2} - \frac{y}{2}$

Subtract $45$ from $36$ .

$- 9 y = - 9$

$x = \frac{9}{2} - \frac{y}{2}$

$- 9 y = - 9$

$x = \frac{9}{2} - \frac{y}{2}$

Divide each term in $- 9 y = - 9$ by $- 9$ and simplify.

Divide each term in $- 9 y = - 9$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = \frac{9}{2} - \frac{y}{2}$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 9}$

$x = \frac{9}{2} - \frac{y}{2}$

$y = \frac{- 9}{- 9}$

$x = \frac{9}{2} - \frac{y}{2}$

$y = \frac{- 9}{- 9}$

$x = \frac{9}{2} - \frac{y}{2}$

Simplify the right side.

Divide $- 9$ by $- 9$ .

$y = 1$

$x = \frac{9}{2} - \frac{y}{2}$

$y = 1$

$x = \frac{9}{2} - \frac{y}{2}$

$y = 1$

$x = \frac{9}{2} - \frac{y}{2}$

$y = 1$

$x = \frac{9}{2} - \frac{y}{2}$

$y = 1$

$x = \frac{9}{2} - \frac{y}{2}$

Step 4

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

Replace all occurrences of $y$ in $x = \frac{9}{2} - \frac{y}{2}$ with $1$ .

$x = \frac{9}{2} - \frac{1}{2}$

$y = 1$

Simplify the right side.

Simplify $\frac{9}{2} - \frac{1}{2}$ .

Combine the numerators over the common denominator.

$x = \frac{9 - 1}{2}$

$y = 1$

Simplify the expression.

Subtract $1$ from $9$ .

$x = \frac{8}{2}$

$y = 1$

Divide $8$ by $2$ .

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

Step 5

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

$(4, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Step 7

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

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