Solve by Addition/Elimination 3x-7y=27 , -5x+4y=-45

$3 x - 7 y = 27$ , $- 5 x + 4 y = - 45$

Step 1

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

$(5) \cdot (3 x - 7 y) = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

Step 2

Simplify.

Simplify the left side.

Simplify $(5) \cdot (3 x - 7 y)$ .

Apply the distributive property.

$5 (3 x) + 5 (- 7 y) = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

Multiply.

Multiply $3$ by $5$ .

$15 x + 5 (- 7 y) = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

Multiply $- 7$ by $5$ .

$15 x - 35 y = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

$15 x - 35 y = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

$15 x - 35 y = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

$15 x - 35 y = (5) (27)$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

Simplify the right side.

Multiply $5$ by $27$ .

$15 x - 35 y = 135$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

$15 x - 35 y = 135$

$(3) \cdot (- 5 x + 4 y) = (3) (- 45)$

Simplify the left side.

Simplify $(3) \cdot (- 5 x + 4 y)$ .

Apply the distributive property.

$15 x - 35 y = 135$

$3 (- 5 x) + 3 (4 y) = (3) (- 45)$

Multiply.

Multiply $- 5$ by $3$ .

$15 x - 35 y = 135$

$- 15 x + 3 (4 y) = (3) (- 45)$

Multiply $4$ by $3$ .

$15 x - 35 y = 135$

$- 15 x + 12 y = (3) (- 45)$

$15 x - 35 y = 135$

$- 15 x + 12 y = (3) (- 45)$

$15 x - 35 y = 135$

$- 15 x + 12 y = (3) (- 45)$

$15 x - 35 y = 135$

$- 15 x + 12 y = (3) (- 45)$

Simplify the right side.

Multiply $3$ by $- 45$ .

$15 x - 35 y = 135$

$- 15 x + 12 y = - 135$

$15 x - 35 y = 135$

$- 15 x + 12 y = - 135$

$15 x - 35 y = 135$

$- 15 x + 12 y = - 135$

Step 3

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

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

Step 4

Divide each term in $- 23 y = 0$ by $- 23$ and simplify.

Divide each term in $- 23 y = 0$ by $- 23$ .

$\frac{- 23 y}{- 23} = \frac{0}{- 23}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 y}{- 23} = \frac{0}{- 23}$

Divide $y$ by $1$ .

$y = \frac{0}{- 23}$

Simplify the right side.

Divide $0$ by $- 23$ .

$y = 0$

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 $x$ .

$15 x - 35 \cdot 0 = 135$

Simplify $15 x - 35 \cdot 0$ .

Multiply $- 35$ by $0$ .

$15 x + 0 = 135$

Add $15 x$ and $0$ .

$15 x = 135$

Divide each term in $15 x = 135$ by $15$ and simplify.

Divide each term in $15 x = 135$ by $15$ .

$\frac{15 x}{15} = \frac{135}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} = \frac{135}{15}$

Divide $x$ by $1$ .

$x = \frac{135}{15}$

Simplify the right side.

Divide $135$ by $15$ .

$x = 9$

Step 6

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

$(9, 0)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(9, 0)$

Equation Form:

$x = 9, y = 0$

Step 8

Solve by Addition/Elimination 3x-7y=27 , -5x+4y=-45

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