Solve by Addition/Elimination -2x-7y=30 7x+4y=18

$- 2 x - 7 y = 30$ $7 x + 4 y = 18$

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

$(7) \cdot (- 2 x - 7 y) = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$7 (- 2 x) + 7 (- 7 y) = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

Multiply.

Multiply $- 2$ by $7$ .

$- 14 x + 7 (- 7 y) = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

Multiply $- 7$ by $7$ .

$- 14 x - 49 y = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

$- 14 x - 49 y = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

$- 14 x - 49 y = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

$- 14 x - 49 y = (7) (30)$

$(2) \cdot (7 x + 4 y) = (2) (18)$

Simplify the right side.

Multiply $7$ by $30$ .

$- 14 x - 49 y = 210$

$(2) \cdot (7 x + 4 y) = (2) (18)$

$- 14 x - 49 y = 210$

$(2) \cdot (7 x + 4 y) = (2) (18)$

Simplify the left side.

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

Apply the distributive property.

$- 14 x - 49 y = 210$

$2 (7 x) + 2 (4 y) = (2) (18)$

Multiply.

Multiply $7$ by $2$ .

$- 14 x - 49 y = 210$

$14 x + 2 (4 y) = (2) (18)$

Multiply $4$ by $2$ .

$- 14 x - 49 y = 210$

$14 x + 8 y = (2) (18)$

$- 14 x - 49 y = 210$

$14 x + 8 y = (2) (18)$

$- 14 x - 49 y = 210$

$14 x + 8 y = (2) (18)$

$- 14 x - 49 y = 210$

$14 x + 8 y = (2) (18)$

Simplify the right side.

Multiply $2$ by $18$ .

$- 14 x - 49 y = 210$

$14 x + 8 y = 36$

$- 14 x - 49 y = 210$

$14 x + 8 y = 36$

$- 14 x - 49 y = 210$

$14 x + 8 y = 36$

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

	$-$	$1$	$4$	$x$	$-$	$4$	$9$	$y$	$=$	$2$	$1$	$0$
$+$		$1$	$4$	$x$	$+$		$8$	$y$	$=$		$3$	$6$
					$-$	$4$	$1$	$y$	$=$	$2$	$4$	$6$

Divide each term in $- 41 y = 246$ by $- 41$ and simplify.

Divide each term in $- 41 y = 246$ by $- 41$ .

$\frac{- 41 y}{- 41} = \frac{246}{- 41}$

Simplify the left side.

Cancel the common factor of $- 41$ .

Cancel the common factor.

$\frac{- 41 y}{- 41} = \frac{246}{- 41}$

Divide $y$ by $1$ .

$y = \frac{246}{- 41}$

Simplify the right side.

Divide $246$ by $- 41$ .

$y = - 6$

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 $x$ .

$- 14 x - 49 \cdot - 6 = 210$

Multiply $- 49$ by $- 6$ .

$- 14 x + 294 = 210$

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

Subtract $294$ from both sides of the equation.

$- 14 x = 210 - 294$

Subtract $294$ from $210$ .

$- 14 x = - 84$

Divide each term in $- 14 x = - 84$ by $- 14$ and simplify.

Divide each term in $- 14 x = - 84$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 84}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 84}{- 14}$

Divide $x$ by $1$ .

$x = \frac{- 84}{- 14}$

Simplify the right side.

Divide $- 84$ by $- 14$ .

$x = 6$

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

$(6, - 6)$

The result can be shown in multiple forms.

Point Form:

$(6, - 6)$

Equation Form:

$x = 6, y = - 6$

Solve by Addition/Elimination -2x-7y=30 7x+4y=18

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