Solve by Addition/Elimination -2x+5y=13 16x+3y=25

$- 2 x + 5 y = 13$ $16 x + 3 y = 25$

Step 1

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

$(- 3) \cdot (- 2 x + 5 y) = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 3 (- 2 x) - 3 (5 y) = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

Multiply.

Multiply $- 2$ by $- 3$ .

$6 x - 3 (5 y) = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

Multiply $5$ by $- 3$ .

$6 x - 15 y = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

$6 x - 15 y = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

$6 x - 15 y = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

$6 x - 15 y = (- 3) (13)$

$(5) \cdot (16 x + 3 y) = (5) (25)$

Simplify the right side.

Multiply $- 3$ by $13$ .

$6 x - 15 y = - 39$

$(5) \cdot (16 x + 3 y) = (5) (25)$

$6 x - 15 y = - 39$

$(5) \cdot (16 x + 3 y) = (5) (25)$

Simplify the left side.

Simplify $(5) \cdot (16 x + 3 y)$ .

Apply the distributive property.

$6 x - 15 y = - 39$

$5 (16 x) + 5 (3 y) = (5) (25)$

Multiply.

Multiply $16$ by $5$ .

$6 x - 15 y = - 39$

$80 x + 5 (3 y) = (5) (25)$

Multiply $3$ by $5$ .

$6 x - 15 y = - 39$

$80 x + 15 y = (5) (25)$

$6 x - 15 y = - 39$

$80 x + 15 y = (5) (25)$

$6 x - 15 y = - 39$

$80 x + 15 y = (5) (25)$

$6 x - 15 y = - 39$

$80 x + 15 y = (5) (25)$

Simplify the right side.

Multiply $5$ by $25$ .

$6 x - 15 y = - 39$

$80 x + 15 y = 125$

$6 x - 15 y = - 39$

$80 x + 15 y = 125$

$6 x - 15 y = - 39$

$80 x + 15 y = 125$

Step 3

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

		$6$	$x$	$-$	$1$	$5$	$y$	$=$	$-$	$3$	$9$
$+$	$8$	$0$	$x$	$+$	$1$	$5$	$y$	$=$	$1$	$2$	$5$
	$8$	$6$	$x$					$=$		$8$	$6$

Step 4

Divide each term in $86 x = 86$ by $86$ and simplify.

Divide each term in $86 x = 86$ by $86$ .

$\frac{86 x}{86} = \frac{86}{86}$

Simplify the left side.

Cancel the common factor of $86$ .

Cancel the common factor.

$\frac{86 x}{86} = \frac{86}{86}$

Divide $x$ by $1$ .

$x = \frac{86}{86}$

Simplify the right side.

Divide $86$ by $86$ .

$x = 1$

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 $y$ .

$6 (1) - 15 y = - 39$

Multiply $6$ by $1$ .

$6 - 15 y = - 39$

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

Subtract $6$ from both sides of the equation.

$- 15 y = - 39 - 6$

Subtract $6$ from $- 39$ .

$- 15 y = - 45$

Divide each term in $- 15 y = - 45$ by $- 15$ and simplify.

Divide each term in $- 15 y = - 45$ by $- 15$ .

$\frac{- 15 y}{- 15} = \frac{- 45}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 y}{- 15} = \frac{- 45}{- 15}$

Divide $y$ by $1$ .

$y = \frac{- 45}{- 15}$

Simplify the right side.

Divide $- 45$ by $- 15$ .

$y = 3$

Step 6

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

$(1, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 8

Solve by Addition/Elimination -2x+5y=13 16x+3y=25

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