Solve by Addition/Elimination 4x+5y=22 2x+3y=12

$4 x + 5 y = 22$ $2 x + 3 y = 12$

Step 1

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

$4 x + 5 y = 22$

$(- 2) \cdot (2 x + 3 y) = (- 2) (12)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$4 x + 5 y = 22$

$- 2 (2 x) - 2 (3 y) = (- 2) (12)$

Multiply.

Multiply $2$ by $- 2$ .

$4 x + 5 y = 22$

$- 4 x - 2 (3 y) = (- 2) (12)$

Multiply $3$ by $- 2$ .

$4 x + 5 y = 22$

$- 4 x - 6 y = (- 2) (12)$

$4 x + 5 y = 22$

$- 4 x - 6 y = (- 2) (12)$

$4 x + 5 y = 22$

$- 4 x - 6 y = (- 2) (12)$

$4 x + 5 y = 22$

$- 4 x - 6 y = (- 2) (12)$

Simplify the right side.

Multiply $- 2$ by $12$ .

$4 x + 5 y = 22$

$- 4 x - 6 y = - 24$

$4 x + 5 y = 22$

$- 4 x - 6 y = - 24$

$4 x + 5 y = 22$

$- 4 x - 6 y = - 24$

Step 3

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

		$4$	$x$	$+$	$5$	$y$	$=$		$2$	$2$
$+$	$-$	$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$	$4$
					$-$	$y$	$=$		$-$	$2$

Step 4

Divide each term in $- y = - 2$ by $- 1$ and simplify.

Divide each term in $- y = - 2$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 2}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$y = 2$

Step 5

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 $x$ .

$4 x + 5 (2) = 22$

Multiply $5$ by $2$ .

$4 x + 10 = 22$

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

Subtract $10$ from both sides of the equation.

$4 x = 22 - 10$

Subtract $10$ from $22$ .

$4 x = 12$

Divide each term in $4 x = 12$ by $4$ and simplify.

Divide each term in $4 x = 12$ by $4$ .

$\frac{4 x}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{12}{4}$

Divide $x$ by $1$ .

$x = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$x = 3$

Step 6

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

$(3, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 8

Solve by Addition/Elimination 4x+5y=22 2x+3y=12

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