Solve by Addition/Elimination 7x+4y=39 2x+4y=14

$7 x + 4 y = 39$ $2 x + 4 y = 14$

Step 1

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

$(- 1) \cdot (7 x + 4 y) = (- 1) (39)$

$2 x + 4 y = 14$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (7 x + 4 y)$ .

Apply the distributive property.

$- 1 (7 x) - 1 (4 y) = (- 1) (39)$

$2 x + 4 y = 14$

Multiply.

Multiply $7$ by $- 1$ .

$- 7 x - 1 (4 y) = (- 1) (39)$

$2 x + 4 y = 14$

Multiply $4$ by $- 1$ .

$- 7 x - 4 y = (- 1) (39)$

$2 x + 4 y = 14$

$- 7 x - 4 y = (- 1) (39)$

$2 x + 4 y = 14$

$- 7 x - 4 y = (- 1) (39)$

$2 x + 4 y = 14$

$- 7 x - 4 y = (- 1) (39)$

$2 x + 4 y = 14$

Simplify the right side.

Multiply $- 1$ by $39$ .

$- 7 x - 4 y = - 39$

$2 x + 4 y = 14$

$- 7 x - 4 y = - 39$

$2 x + 4 y = 14$

$- 7 x - 4 y = - 39$

$2 x + 4 y = 14$

Step 3

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

	$-$	$7$	$x$	$-$	$4$	$y$	$=$	$-$	$3$	$9$
$+$		$2$	$x$	$+$	$4$	$y$	$=$		$1$	$4$
	$-$	$5$	$x$				$=$	$-$	$2$	$5$

Step 4

Divide each term in $- 5 x = - 25$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 25$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 5}$

Simplify the right side.

Divide $- 25$ by $- 5$ .

$x = 5$

Step 5

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 $y$ .

$- 7 \cdot 5 - 4 y = - 39$

Multiply $- 7$ by $5$ .

$- 35 - 4 y = - 39$

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

Add $35$ to both sides of the equation.

$- 4 y = - 39 + 35$

Add $- 39$ and $35$ .

$- 4 y = - 4$

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

Divide each term in $- 4 y = - 4$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$y = 1$

Step 6

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

$(5, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 1)$

Equation Form:

$x = 5, y = 1$

Step 8

Solve by Addition/Elimination 7x+4y=39 2x+4y=14

Related Questions

Support LCMGCF.com by disabling your adblocker.