Solve by Addition/Elimination 2x+5y=16 3x-5y=-1

$2 x + 5 y = 16$ $3 x - 5 y = - 1$

Step 1

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

	$2$	$x$	$+$	$5$	$y$	$=$	$1$	$6$
$+$	$3$	$x$	$-$	$5$	$y$	$=$	$-$	$1$
	$5$	$x$				$=$	$1$	$5$

Step 2

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$

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 $y$ .

$2 (3) + 5 y = 16$

Multiply $2$ by $3$ .

$6 + 5 y = 16$

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

Subtract $6$ from both sides of the equation.

$5 y = 16 - 6$

Subtract $6$ from $16$ .

$5 y = 10$

Divide each term in $5 y = 10$ by $5$ and simplify.

Divide each term in $5 y = 10$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10}{5}$

Divide $y$ by $1$ .

$y = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$y = 2$

Step 4

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

$(3, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 6

Solve by Addition/Elimination 2x+5y=16 3x-5y=-1

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