Solve by Addition/Elimination 3x+5y=3 x+2y=0

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

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

$3 x + 5 y = 3$

$(- 3) \cdot (x + 2 y) = (- 3) (0)$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 x + 5 y = 3$

$- 3 x - 3 (2 y) = (- 3) (0)$

Multiply $2$ by $- 3$ .

$3 x + 5 y = 3$

$- 3 x - 6 y = (- 3) (0)$

$3 x + 5 y = 3$

$- 3 x - 6 y = (- 3) (0)$

$3 x + 5 y = 3$

$- 3 x - 6 y = (- 3) (0)$

Simplify the right side.

Multiply $- 3$ by $0$ .

$3 x + 5 y = 3$

$- 3 x - 6 y = 0$

$3 x + 5 y = 3$

$- 3 x - 6 y = 0$

$3 x + 5 y = 3$

$- 3 x - 6 y = 0$

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

		$3$	$x$	$+$	$5$	$y$	$=$	$3$
$+$	$-$	$3$	$x$	$-$	$6$	$y$	$=$	$0$
					$-$	$y$	$=$	$3$

Divide each term in $- y = 3$ by $- 1$ and simplify.

Divide each term in $- y = 3$ by $- 1$ .

$\frac{- y}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{3}{- 1}$

Divide $y$ by $1$ .

$y = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$y = - 3$

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 $x$ .

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

Multiply $5$ by $- 3$ .

$3 x - 15 = 3$

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

Add $15$ to both sides of the equation.

$3 x = 3 + 15$

Add $3$ and $15$ .

$3 x = 18$

Divide each term in $3 x = 18$ by $3$ and simplify.

Divide each term in $3 x = 18$ by $3$ .

$\frac{3 x}{3} = \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{18}{3}$

Divide $x$ by $1$ .

$x = \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$x = 6$

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

$(6, - 3)$

The result can be shown in multiple forms.

Point Form:

$(6, - 3)$

Equation Form:

$x = 6, y = - 3$

Solve by Addition/Elimination 3x+5y=3 x+2y=0

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