Solve by Addition/Elimination -4x+7y=9 2y=-5x-22

$- 4 x + 7 y = 9$ $2 y = - 5 x - 22$

Step 1

Add $5 x$ to both sides of the equation.

$- 4 x + 7 y = 9, 2 y + 5 x = - 22$

Step 2

Reorder the polynomial.

$5 x + 2 y = - 22$

$- 4 x + 7 y = 9$

Step 3

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

$(- 2) \cdot (- 4 x + 7 y) = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (- 4 x + 7 y)$ .

Apply the distributive property.

$- 2 (- 4 x) - 2 (7 y) = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

Multiply.

Multiply $- 4$ by $- 2$ .

$8 x - 2 (7 y) = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

Multiply $7$ by $- 2$ .

$8 x - 14 y = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

$8 x - 14 y = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

$8 x - 14 y = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

$8 x - 14 y = (- 2) (9)$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

Simplify the right side.

Multiply $- 2$ by $9$ .

$8 x - 14 y = - 18$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

$8 x - 14 y = - 18$

$(7) \cdot (5 x + 2 y) = (7) (- 22)$

Simplify the left side.

Simplify $(7) \cdot (5 x + 2 y)$ .

Apply the distributive property.

$8 x - 14 y = - 18$

$7 (5 x) + 7 (2 y) = (7) (- 22)$

Multiply.

Multiply $5$ by $7$ .

$8 x - 14 y = - 18$

$35 x + 7 (2 y) = (7) (- 22)$

Multiply $2$ by $7$ .

$8 x - 14 y = - 18$

$35 x + 14 y = (7) (- 22)$

$8 x - 14 y = - 18$

$35 x + 14 y = (7) (- 22)$

$8 x - 14 y = - 18$

$35 x + 14 y = (7) (- 22)$

$8 x - 14 y = - 18$

$35 x + 14 y = (7) (- 22)$

Simplify the right side.

Multiply $7$ by $- 22$ .

$8 x - 14 y = - 18$

$35 x + 14 y = - 154$

$8 x - 14 y = - 18$

$35 x + 14 y = - 154$

$8 x - 14 y = - 18$

$35 x + 14 y = - 154$

Step 5

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

		$8$	$x$	$-$	$1$	$4$	$y$	$=$		$-$	$1$	$8$
$+$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$	$-$	$1$	$5$	$4$
	$4$	$3$	$x$					$=$	$-$	$1$	$7$	$2$

Step 6

Divide each term in $43 x = - 172$ by $43$ and simplify.

Divide each term in $43 x = - 172$ by $43$ .

$\frac{43 x}{43} = \frac{- 172}{43}$

Simplify the left side.

Cancel the common factor of $43$ .

Cancel the common factor.

$\frac{43 x}{43} = \frac{- 172}{43}$

Divide $x$ by $1$ .

$x = \frac{- 172}{43}$

Simplify the right side.

Divide $- 172$ by $43$ .

$x = - 4$

Step 7

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 $y$ .

$8 (- 4) - 14 y = - 18$

Multiply $8$ by $- 4$ .

$- 32 - 14 y = - 18$

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

Add $32$ to both sides of the equation.

$- 14 y = - 18 + 32$

Add $- 18$ and $32$ .

$- 14 y = 14$

Divide each term in $- 14 y = 14$ by $- 14$ and simplify.

Divide each term in $- 14 y = 14$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{14}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{14}{- 14}$

Divide $y$ by $1$ .

$y = \frac{14}{- 14}$

Simplify the right side.

Divide $14$ by $- 14$ .

$y = - 1$

Step 8

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

$(- 4, - 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 10

Solve by Addition/Elimination -4x+7y=9 2y=-5x-22

Related Questions

Support LCMGCF.com by disabling your adblocker.