Solve by Addition/Elimination 4x+5y=51 , 4x+2y=66

$4 x + 5 y = 51$ , $4 x + 2 y = 66$

Step 1

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

$(- 1) \cdot (4 x + 5 y) = (- 1) (51)$

$4 x + 2 y = 66$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (4 x + 5 y)$ .

Apply the distributive property.

$- 1 (4 x) - 1 (5 y) = (- 1) (51)$

$4 x + 2 y = 66$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (5 y) = (- 1) (51)$

$4 x + 2 y = 66$

Multiply $5$ by $- 1$ .

$- 4 x - 5 y = (- 1) (51)$

$4 x + 2 y = 66$

$- 4 x - 5 y = (- 1) (51)$

$4 x + 2 y = 66$

$- 4 x - 5 y = (- 1) (51)$

$4 x + 2 y = 66$

$- 4 x - 5 y = (- 1) (51)$

$4 x + 2 y = 66$

Simplify the right side.

Multiply $- 1$ by $51$ .

$- 4 x - 5 y = - 51$

$4 x + 2 y = 66$

$- 4 x - 5 y = - 51$

$4 x + 2 y = 66$

$- 4 x - 5 y = - 51$

$4 x + 2 y = 66$

Step 3

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

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

Step 4

Divide each term in $- 3 y = 15$ by $- 3$ and simplify.

Divide each term in $- 3 y = 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Divide $y$ by $1$ .

$y = \frac{15}{- 3}$

Simplify the right side.

Divide $15$ by $- 3$ .

$y = - 5$

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 $x$ .

$- 4 x - 5 \cdot - 5 = - 51$

Multiply $- 5$ by $- 5$ .

$- 4 x + 25 = - 51$

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

Subtract $25$ from both sides of the equation.

$- 4 x = - 51 - 25$

Subtract $25$ from $- 51$ .

$- 4 x = - 76$

Divide each term in $- 4 x = - 76$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 76$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 76}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 76}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 76}{- 4}$

Simplify the right side.

Divide $- 76$ by $- 4$ .

$x = 19$

Step 6

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

$(19, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(19, - 5)$

Equation Form:

$x = 19, y = - 5$

Step 8

Solve by Addition/Elimination 4x+5y=51 , 4x+2y=66

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