Solve by Addition/Elimination 5x+3y=-3 , 2x-3y=24

$5 x + 3 y = - 3$ , $2 x - 3 y = 24$

Step 1

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

	$5$	$x$	$+$	$3$	$y$	$=$	$-$	$3$
$+$	$2$	$x$	$-$	$3$	$y$	$=$	$2$	$4$
	$7$	$x$				$=$	$2$	$1$

Step 2

Divide each term in $7 x = 21$ by $7$ and simplify.

Divide each term in $7 x = 21$ by $7$ .

$\frac{7 x}{7} = \frac{21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{21}{7}$

Divide $x$ by $1$ .

$x = \frac{21}{7}$

Simplify the right side.

Divide $21$ by $7$ .

$x = 3$

Step 3

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 $y$ .

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

Multiply $5$ by $3$ .

$15 + 3 y = - 3$

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

Subtract $15$ from both sides of the equation.

$3 y = - 3 - 15$

Subtract $15$ from $- 3$ .

$3 y = - 18$

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

Divide each term in $3 y = - 18$ by $3$ .

$\frac{3 y}{3} = \frac{- 18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 18}{3}$

Divide $y$ by $1$ .

$y = \frac{- 18}{3}$

Simplify the right side.

Divide $- 18$ by $3$ .

$y = - 6$

Step 4

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

$(3, - 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, - 6)$

Equation Form:

$x = 3, y = - 6$

Step 6

Solve by Addition/Elimination 5x+3y=-3 , 2x-3y=24

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