Solve by Addition/Elimination 3x-9y=4 , 5x-5y=4

$3 x - 9 y = 4$ , $5 x - 5 y = 4$

Step 1

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

$(- 5) \cdot (3 x - 9 y) = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 5) \cdot (3 x - 9 y)$ .

Apply the distributive property.

$- 5 (3 x) - 5 (- 9 y) = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

Multiply.

Multiply $3$ by $- 5$ .

$- 15 x - 5 (- 9 y) = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

Multiply $- 9$ by $- 5$ .

$- 15 x + 45 y = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

$- 15 x + 45 y = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

$- 15 x + 45 y = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

$- 15 x + 45 y = (- 5) (4)$

$(3) \cdot (5 x - 5 y) = (3) (4)$

Simplify the right side.

Multiply $- 5$ by $4$ .

$- 15 x + 45 y = - 20$

$(3) \cdot (5 x - 5 y) = (3) (4)$

$- 15 x + 45 y = - 20$

$(3) \cdot (5 x - 5 y) = (3) (4)$

Simplify the left side.

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

Apply the distributive property.

$- 15 x + 45 y = - 20$

$3 (5 x) + 3 (- 5 y) = (3) (4)$

Multiply.

Multiply $5$ by $3$ .

$- 15 x + 45 y = - 20$

$15 x + 3 (- 5 y) = (3) (4)$

Multiply $- 5$ by $3$ .

$- 15 x + 45 y = - 20$

$15 x - 15 y = (3) (4)$

$- 15 x + 45 y = - 20$

$15 x - 15 y = (3) (4)$

$- 15 x + 45 y = - 20$

$15 x - 15 y = (3) (4)$

$- 15 x + 45 y = - 20$

$15 x - 15 y = (3) (4)$

Simplify the right side.

Multiply $3$ by $4$ .

$- 15 x + 45 y = - 20$

$15 x - 15 y = 12$

$- 15 x + 45 y = - 20$

$15 x - 15 y = 12$

$- 15 x + 45 y = - 20$

$15 x - 15 y = 12$

Step 3

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

	$-$	$1$	$5$	$x$	$+$	$4$	$5$	$y$	$=$	$-$	$2$	$0$
$+$		$1$	$5$	$x$	$-$	$1$	$5$	$y$	$=$		$1$	$2$
						$3$	$0$	$y$	$=$		$-$	$8$

Step 4

Divide each term in $30 y = - 8$ by $30$ and simplify.

Divide each term in $30 y = - 8$ by $30$ .

$\frac{30 y}{30} = \frac{- 8}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 y}{30} = \frac{- 8}{30}$

Divide $y$ by $1$ .

$y = \frac{- 8}{30}$

Simplify the right side.

Cancel the common factor of $- 8$ and $30$ .

Factor $2$ out of $- 8$ .

$y = \frac{2 (- 4)}{30}$

Cancel the common factors.

Factor $2$ out of $30$ .

$y = \frac{2 \cdot - 4}{2 \cdot 15}$

Cancel the common factor.

$y = \frac{2 \cdot - 4}{2 \cdot 15}$

Rewrite the expression.

$y = \frac{- 4}{15}$

Move the negative in front of the fraction.

$y = - \frac{4}{15}$

Step 5

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

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

$- 15 x + 45 (- \frac{4}{15}) = - 20$

Simplify each term.

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{4}{15}$ into the numerator.

$- 15 x + 45 (\frac{- 4}{15}) = - 20$

Factor $15$ out of $45$ .

$- 15 x + 15 (3) \frac{- 4}{15} = - 20$

Cancel the common factor.

$- 15 x + 15 \cdot 3 \frac{- 4}{15} = - 20$

Rewrite the expression.

$- 15 x + 3 \cdot - 4 = - 20$

Multiply $3$ by $- 4$ .

$- 15 x - 12 = - 20$

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

Add $12$ to both sides of the equation.

$- 15 x = - 20 + 12$

Add $- 20$ and $12$ .

$- 15 x = - 8$

Divide each term in $- 15 x = - 8$ by $- 15$ and simplify.

Divide each term in $- 15 x = - 8$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{- 8}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{- 8}{- 15}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 15}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{8}{15}$

Step 6

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

$(\frac{8}{15}, - \frac{4}{15})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(\frac{8}{15}, - \frac{4}{15})$

Equation Form:

$x = \frac{8}{15}, y = - \frac{4}{15}$

Step 8

Solve by Addition/Elimination 3x-9y=4 , 5x-5y=4

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