Solve by Addition/Elimination 5x+3y=58 5x-3y=22

$5 x + 3 y = 58$ $5 x - 3 y = 22$

Step 1

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

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

Step 2

Divide each term in $10 x = 80$ by $10$ and simplify.

Divide each term in $10 x = 80$ by $10$ .

$\frac{10 x}{10} = \frac{80}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{80}{10}$

Divide $x$ by $1$ .

$x = \frac{80}{10}$

Simplify the right side.

Divide $80$ by $10$ .

$x = 8$

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 $y$ .

$5 (8) + 3 y = 58$

Multiply $5$ by $8$ .

$40 + 3 y = 58$

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

Subtract $40$ from both sides of the equation.

$3 y = 58 - 40$

Subtract $40$ from $58$ .

$3 y = 18$

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.

$(8, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(8, 6)$

Equation Form:

$x = 8, y = 6$

Step 6

Solve by Addition/Elimination 5x+3y=58 5x-3y=22

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