Solve by Addition/Elimination -7y-4x=1 7y-2x=53

$- 7 y - 4 x = 1$ $7 y - 2 x = 53$

Step 1

Simplify the left side.

Reorder $- 7 y$ and $- 4 x$ .

$- 4 x - 7 y = 1$

$7 y - 2 x = 53$

$- 4 x - 7 y = 1$

$7 y - 2 x = 53$

Step 2

Simplify the left side.

Reorder $7 y$ and $- 2 x$ .

$- 2 x + 7 y = 53$

$- 4 x - 7 y = 1$

$- 2 x + 7 y = 53$

$- 4 x - 7 y = 1$

Step 3

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

$- 4 x - 7 y = 1$

$(- 2) \cdot (- 2 x + 7 y) = (- 2) (53)$

Step 4

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 4 x - 7 y = 1$

$- 2 (- 2 x) - 2 (7 y) = (- 2) (53)$

Multiply.

Multiply $- 2$ by $- 2$ .

$- 4 x - 7 y = 1$

$4 x - 2 (7 y) = (- 2) (53)$

Multiply $7$ by $- 2$ .

$- 4 x - 7 y = 1$

$4 x - 14 y = (- 2) (53)$

$- 4 x - 7 y = 1$

$4 x - 14 y = (- 2) (53)$

$- 4 x - 7 y = 1$

$4 x - 14 y = (- 2) (53)$

$- 4 x - 7 y = 1$

$4 x - 14 y = (- 2) (53)$

Simplify the right side.

Multiply $- 2$ by $53$ .

$- 4 x - 7 y = 1$

$4 x - 14 y = - 106$

$- 4 x - 7 y = 1$

$4 x - 14 y = - 106$

$- 4 x - 7 y = 1$

$4 x - 14 y = - 106$

Step 5

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

	$-$	$4$	$x$		$-$	$7$	$y$	$=$				$1$
$+$		$4$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$1$	$0$	$6$
				$-$	$2$	$1$	$y$	$=$	$-$	$1$	$0$	$5$

Step 6

Divide each term in $- 21 y = - 105$ by $- 21$ and simplify.

Divide each term in $- 21 y = - 105$ by $- 21$ .

$\frac{- 21 y}{- 21} = \frac{- 105}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 y}{- 21} = \frac{- 105}{- 21}$

Divide $y$ by $1$ .

$y = \frac{- 105}{- 21}$

Simplify the right side.

Divide $- 105$ by $- 21$ .

$y = 5$

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 $x$ .

$- 4 x - 7 \cdot 5 = 1$

Multiply $- 7$ by $5$ .

$- 4 x - 35 = 1$

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

Add $35$ to both sides of the equation.

$- 4 x = 1 + 35$

Add $1$ and $35$ .

$- 4 x = 36$

Divide each term in $- 4 x = 36$ by $- 4$ and simplify.

Divide each term in $- 4 x = 36$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{36}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{36}{- 4}$

Divide $x$ by $1$ .

$x = \frac{36}{- 4}$

Simplify the right side.

Divide $36$ by $- 4$ .

$x = - 9$

Step 8

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

$(- 9, 5)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 9, 5)$

Equation Form:

$x = - 9, y = 5$

Step 10

Solve by Addition/Elimination -7y-4x=1 7y-2x=53

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