Solve by Addition/Elimination 7x-4y=33 6x-7y=14

$7 x - 4 y = 33$ $6 x - 7 y = 14$

Step 1

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

$(- 7) \cdot (7 x - 4 y) = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 7 (7 x) - 7 (- 4 y) = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

Multiply.

Multiply $7$ by $- 7$ .

$- 49 x - 7 (- 4 y) = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

Multiply $- 4$ by $- 7$ .

$- 49 x + 28 y = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

$- 49 x + 28 y = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

$- 49 x + 28 y = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

$- 49 x + 28 y = (- 7) (33)$

$(4) \cdot (6 x - 7 y) = (4) (14)$

Simplify the right side.

Multiply $- 7$ by $33$ .

$- 49 x + 28 y = - 231$

$(4) \cdot (6 x - 7 y) = (4) (14)$

$- 49 x + 28 y = - 231$

$(4) \cdot (6 x - 7 y) = (4) (14)$

Simplify the left side.

Simplify $(4) \cdot (6 x - 7 y)$ .

Apply the distributive property.

$- 49 x + 28 y = - 231$

$4 (6 x) + 4 (- 7 y) = (4) (14)$

Multiply.

Multiply $6$ by $4$ .

$- 49 x + 28 y = - 231$

$24 x + 4 (- 7 y) = (4) (14)$

Multiply $- 7$ by $4$ .

$- 49 x + 28 y = - 231$

$24 x - 28 y = (4) (14)$

$- 49 x + 28 y = - 231$

$24 x - 28 y = (4) (14)$

$- 49 x + 28 y = - 231$

$24 x - 28 y = (4) (14)$

$- 49 x + 28 y = - 231$

$24 x - 28 y = (4) (14)$

Simplify the right side.

Multiply $4$ by $14$ .

$- 49 x + 28 y = - 231$

$24 x - 28 y = 56$

$- 49 x + 28 y = - 231$

$24 x - 28 y = 56$

$- 49 x + 28 y = - 231$

$24 x - 28 y = 56$

Step 3

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

	$-$	$4$	$9$	$x$	$+$	$2$	$8$	$y$	$=$	$-$	$2$	$3$	$1$
$+$		$2$	$4$	$x$	$-$	$2$	$8$	$y$	$=$			$5$	$6$
	$-$	$2$	$5$	$x$					$=$	$-$	$1$	$7$	$5$

Step 4

Divide each term in $- 25 x = - 175$ by $- 25$ and simplify.

Divide each term in $- 25 x = - 175$ by $- 25$ .

$\frac{- 25 x}{- 25} = \frac{- 175}{- 25}$

Simplify the left side.

Cancel the common factor of $- 25$ .

Cancel the common factor.

$\frac{- 25 x}{- 25} = \frac{- 175}{- 25}$

Divide $x$ by $1$ .

$x = \frac{- 175}{- 25}$

Simplify the right side.

Divide $- 175$ by $- 25$ .

$x = 7$

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 $y$ .

$- 49 \cdot 7 + 28 y = - 231$

Multiply $- 49$ by $7$ .

$- 343 + 28 y = - 231$

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

Add $343$ to both sides of the equation.

$28 y = - 231 + 343$

Add $- 231$ and $343$ .

$28 y = 112$

Divide each term in $28 y = 112$ by $28$ and simplify.

Divide each term in $28 y = 112$ by $28$ .

$\frac{28 y}{28} = \frac{112}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 y}{28} = \frac{112}{28}$

Divide $y$ by $1$ .

$y = \frac{112}{28}$

Simplify the right side.

Divide $112$ by $28$ .

$y = 4$

Step 6

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

$(7, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(7, 4)$

Equation Form:

$x = 7, y = 4$

Step 8

Solve by Addition/Elimination 7x-4y=33 6x-7y=14

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