Solve by Addition/Elimination 3x+5y=48 -3x+5y=12

$3 x + 5 y = 48$ $- 3 x + 5 y = 12$

Step 1

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

		$3$	$x$	$+$	$5$	$y$	$=$	$4$	$8$
$+$	$-$	$3$	$x$	$+$	$5$	$y$	$=$	$1$	$2$
				$1$	$0$	$y$	$=$	$6$	$0$

Step 2

Divide each term in $10 y = 60$ by $10$ and simplify.

Divide each term in $10 y = 60$ by $10$ .

$\frac{10 y}{10} = \frac{60}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{60}{10}$

Divide $y$ by $1$ .

$y = \frac{60}{10}$

Simplify the right side.

Divide $60$ by $10$ .

$y = 6$

Step 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 $x$ .

$3 x + 5 (6) = 48$

Multiply $5$ by $6$ .

$3 x + 30 = 48$

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

Subtract $30$ from both sides of the equation.

$3 x = 48 - 30$

Subtract $30$ from $48$ .

$3 x = 18$

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 $3$ .

$x = 6$

Step 4

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

$(6, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(6, 6)$

Equation Form:

$x = 6, y = 6$

Step 6

Solve by Addition/Elimination 3x+5y=48 -3x+5y=12

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