Solve by Addition/Elimination -5y+4x=49 7y+2x=-23

$- 5 y + 4 x = 49$ $7 y + 2 x = - 23$

Step 1

Simplify the left side.

Reorder $- 5 y$ and $4 x$ .

$4 x - 5 y = 49$

$7 y + 2 x = - 23$

$4 x - 5 y = 49$

$7 y + 2 x = - 23$

Step 2

Simplify the left side.

Reorder $7 y$ and $2 x$ .

$2 x + 7 y = - 23$

$4 x - 5 y = 49$

$2 x + 7 y = - 23$

$4 x - 5 y = 49$

Step 3

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

$4 x - 5 y = 49$

$(- 2) \cdot (2 x + 7 y) = (- 2) (- 23)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (2 x + 7 y)$ .

Apply the distributive property.

$4 x - 5 y = 49$

$- 2 (2 x) - 2 (7 y) = (- 2) (- 23)$

Multiply.

Multiply $2$ by $- 2$ .

$4 x - 5 y = 49$

$- 4 x - 2 (7 y) = (- 2) (- 23)$

Multiply $7$ by $- 2$ .

$4 x - 5 y = 49$

$- 4 x - 14 y = (- 2) (- 23)$

$4 x - 5 y = 49$

$- 4 x - 14 y = (- 2) (- 23)$

$4 x - 5 y = 49$

$- 4 x - 14 y = (- 2) (- 23)$

$4 x - 5 y = 49$

$- 4 x - 14 y = (- 2) (- 23)$

Simplify the right side.

Multiply $- 2$ by $- 23$ .

$4 x - 5 y = 49$

$- 4 x - 14 y = 46$

$4 x - 5 y = 49$

$- 4 x - 14 y = 46$

$4 x - 5 y = 49$

$- 4 x - 14 y = 46$

Step 5

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

		$4$	$x$		$-$	$5$	$y$	$=$	$4$	$9$
$+$	$-$	$4$	$x$	$-$	$1$	$4$	$y$	$=$	$4$	$6$
				$-$	$1$	$9$	$y$	$=$	$9$	$5$

Step 6

Divide each term in $- 19 y = 95$ by $- 19$ and simplify.

Divide each term in $- 19 y = 95$ by $- 19$ .

$\frac{- 19 y}{- 19} = \frac{95}{- 19}$

Simplify the left side.

Cancel the common factor of $- 19$ .

Cancel the common factor.

$\frac{- 19 y}{- 19} = \frac{95}{- 19}$

Divide $y$ by $1$ .

$y = \frac{95}{- 19}$

Simplify the right side.

Divide $95$ by $- 19$ .

$y = - 5$

Step 7

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 $x$ .

$4 x - 5 \cdot - 5 = 49$

Multiply $- 5$ by $- 5$ .

$4 x + 25 = 49$

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

Subtract $25$ from both sides of the equation.

$4 x = 49 - 25$

Subtract $25$ from $49$ .

$4 x = 24$

Divide each term in $4 x = 24$ by $4$ and simplify.

Divide each term in $4 x = 24$ by $4$ .

$\frac{4 x}{4} = \frac{24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{24}{4}$

Divide $x$ by $1$ .

$x = \frac{24}{4}$

Simplify the right side.

Divide $24$ by $4$ .

$x = 6$

Step 8

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

$(6, - 5)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(6, - 5)$

Equation Form:

$x = 6, y = - 5$

Step 10

Solve by Addition/Elimination -5y+4x=49 7y+2x=-23

Related Questions

Support LCMGCF.com by disabling your adblocker.