Solve by Addition/Elimination 5x+2y=7 -2x+6y=9

$5 x + 2 y = 7$ $- 2 x + 6 y = 9$

Step 1

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(- 3) \cdot (5 x + 2 y) = (- 3) (7)$

$- 2 x + 6 y = 9$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (5 x + 2 y)$ .

Apply the distributive property.

$- 3 (5 x) - 3 (2 y) = (- 3) (7)$

$- 2 x + 6 y = 9$

Multiply.

Multiply $5$ by $- 3$ .

$- 15 x - 3 (2 y) = (- 3) (7)$

$- 2 x + 6 y = 9$

Multiply $2$ by $- 3$ .

$- 15 x - 6 y = (- 3) (7)$

$- 2 x + 6 y = 9$

$- 15 x - 6 y = (- 3) (7)$

$- 2 x + 6 y = 9$

$- 15 x - 6 y = (- 3) (7)$

$- 2 x + 6 y = 9$

$- 15 x - 6 y = (- 3) (7)$

$- 2 x + 6 y = 9$

Simplify the right side.

Multiply $- 3$ by $7$ .

$- 15 x - 6 y = - 21$

$- 2 x + 6 y = 9$

$- 15 x - 6 y = - 21$

$- 2 x + 6 y = 9$

$- 15 x - 6 y = - 21$

$- 2 x + 6 y = 9$

Step 3

Add the two equations together to eliminate $y$ from the system.

	$-$	$1$	$5$	$x$	$-$	$6$	$y$	$=$	$-$	$2$	$1$
$+$		$-$	$2$	$x$	$+$	$6$	$y$	$=$			$9$
	$-$	$1$	$7$	$x$				$=$	$-$	$1$	$2$

Step 4

Divide each term in $- 17 x = - 12$ by $- 17$ and simplify.

Divide each term in $- 17 x = - 12$ by $- 17$ .

$\frac{- 17 x}{- 17} = \frac{- 12}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} = \frac{- 12}{- 17}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 17}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{12}{17}$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$- 15 (\frac{12}{17}) - 6 y = - 21$

Simplify each term.

Multiply $- 15 (\frac{12}{17})$ .

Combine $- 15$ and $\frac{12}{17}$ .

$\frac{- 15 \cdot 12}{17} - 6 y = - 21$

Multiply $- 15$ by $12$ .

$\frac{- 180}{17} - 6 y = - 21$

Move the negative in front of the fraction.

$- \frac{180}{17} - 6 y = - 21$

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

Add $\frac{180}{17}$ to both sides of the equation.

$- 6 y = - 21 + \frac{180}{17}$

To write $- 21$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$- 6 y = - 21 \cdot \frac{17}{17} + \frac{180}{17}$

Combine $- 21$ and $\frac{17}{17}$ .

$- 6 y = \frac{- 21 \cdot 17}{17} + \frac{180}{17}$

Combine the numerators over the common denominator.

$- 6 y = \frac{- 21 \cdot 17 + 180}{17}$

Simplify the numerator.

Multiply $- 21$ by $17$ .

$- 6 y = \frac{- 357 + 180}{17}$

Add $- 357$ and $180$ .

$- 6 y = \frac{- 177}{17}$

Move the negative in front of the fraction.

$- 6 y = - \frac{177}{17}$

Divide each term in $- 6 y = - \frac{177}{17}$ by $- 6$ and simplify.

Divide each term in $- 6 y = - \frac{177}{17}$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- \frac{177}{17}}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- \frac{177}{17}}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- \frac{177}{17}}{- 6}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{177}{17} \cdot \frac{1}{- 6}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{177}{17}$ into the numerator.

$y = \frac{- 177}{17} \cdot \frac{1}{- 6}$

Factor $3$ out of $- 177$ .

$y = \frac{3 (- 59)}{17} \cdot \frac{1}{- 6}$

Factor $3$ out of $- 6$ .

$y = \frac{3 \cdot - 59}{17} \cdot \frac{1}{3 \cdot - 2}$

Cancel the common factor.

$y = \frac{3 \cdot - 59}{17} \cdot \frac{1}{3 \cdot - 2}$

Rewrite the expression.

$y = \frac{- 59}{17} \cdot \frac{1}{- 2}$

Multiply $\frac{- 59}{17}$ by $\frac{1}{- 2}$ .

$y = \frac{- 59}{17 \cdot - 2}$

Multiply $17$ by $- 2$ .

$y = \frac{- 59}{- 34}$

Dividing two negative values results in a positive value.

$y = \frac{59}{34}$

Step 6

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

$(\frac{12}{17}, \frac{59}{34})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(\frac{12}{17}, \frac{59}{34})$

Equation Form:

$x = \frac{12}{17}, y = \frac{59}{34}$

Step 8

Solve by Addition/Elimination 5x+2y=7 -2x+6y=9

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