Solve by Addition/Elimination 6x-10y=2 2x+5y=9

$6 x - 10 y = 2$ $2 x + 5 y = 9$

Step 1

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

$6 x - 10 y = 2$

$(- 3) \cdot (2 x + 5 y) = (- 3) (9)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$6 x - 10 y = 2$

$- 3 (2 x) - 3 (5 y) = (- 3) (9)$

Multiply.

Multiply $2$ by $- 3$ .

$6 x - 10 y = 2$

$- 6 x - 3 (5 y) = (- 3) (9)$

Multiply $5$ by $- 3$ .

$6 x - 10 y = 2$

$- 6 x - 15 y = (- 3) (9)$

$6 x - 10 y = 2$

$- 6 x - 15 y = (- 3) (9)$

$6 x - 10 y = 2$

$- 6 x - 15 y = (- 3) (9)$

$6 x - 10 y = 2$

$- 6 x - 15 y = (- 3) (9)$

Simplify the right side.

Multiply $- 3$ by $9$ .

$6 x - 10 y = 2$

$- 6 x - 15 y = - 27$

$6 x - 10 y = 2$

$- 6 x - 15 y = - 27$

$6 x - 10 y = 2$

$- 6 x - 15 y = - 27$

Step 3

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

		$6$	$x$	$-$	$1$	$0$	$y$	$=$			$2$
$+$	$-$	$6$	$x$	$-$	$1$	$5$	$y$	$=$	$-$	$2$	$7$
				$-$	$2$	$5$	$y$	$=$	$-$	$2$	$5$

Step 4

Divide each term in $- 25 y = - 25$ by $- 25$ and simplify.

Divide each term in $- 25 y = - 25$ by $- 25$ .

$\frac{- 25 y}{- 25} = \frac{- 25}{- 25}$

Simplify the left side.

Cancel the common factor of $- 25$ .

Cancel the common factor.

$\frac{- 25 y}{- 25} = \frac{- 25}{- 25}$

Divide $y$ by $1$ .

$y = \frac{- 25}{- 25}$

Simplify the right side.

Divide $- 25$ by $- 25$ .

$y = 1$

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 $x$ .

$6 x - 10 \cdot 1 = 2$

Multiply $- 10$ by $1$ .

$6 x - 10 = 2$

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

Add $10$ to both sides of the equation.

$6 x = 2 + 10$

Add $2$ and $10$ .

$6 x = 12$

Divide each term in $6 x = 12$ by $6$ and simplify.

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

Step 6

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

$(2, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 8

Solve by Addition/Elimination 6x-10y=2 2x+5y=9

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