Solve by Addition/Elimination 4x-10=-6y , 7x+6y=-14

$4 x - 10 = - 6 y$ , $7 x + 6 y = - 14$

Step 1

Move all terms containing variables to the left side of the equation.

Add $6 y$ to both sides of the equation.

$4 x - 10 + 6 y = 0$

$7 x + 6 y = - 14$

Move $- 10$ .

$4 x + 6 y - 10 = 0$

$7 x + 6 y = - 14$

$4 x + 6 y - 10 = 0$

$7 x + 6 y = - 14$

Step 2

Add $10$ to both sides of the equation.

$4 x + 6 y = 10$

$7 x + 6 y = - 14$

Step 3

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

$(- 1) \cdot (4 x + 6 y) = (- 1) (10)$

$7 x + 6 y = - 14$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (4 x + 6 y)$ .

Apply the distributive property.

$- 1 (4 x) - 1 (6 y) = (- 1) (10)$

$7 x + 6 y = - 14$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (6 y) = (- 1) (10)$

$7 x + 6 y = - 14$

Multiply $6$ by $- 1$ .

$- 4 x - 6 y = (- 1) (10)$

$7 x + 6 y = - 14$

$- 4 x - 6 y = (- 1) (10)$

$7 x + 6 y = - 14$

$- 4 x - 6 y = (- 1) (10)$

$7 x + 6 y = - 14$

$- 4 x - 6 y = (- 1) (10)$

$7 x + 6 y = - 14$

Simplify the right side.

Multiply $- 1$ by $10$ .

$- 4 x - 6 y = - 10$

$7 x + 6 y = - 14$

$- 4 x - 6 y = - 10$

$7 x + 6 y = - 14$

$- 4 x - 6 y = - 10$

$7 x + 6 y = - 14$

Step 5

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

	$-$	$4$	$x$	$-$	$6$	$y$	$=$	$-$	$1$	$0$
$+$		$7$	$x$	$+$	$6$	$y$	$=$	$-$	$1$	$4$
		$3$	$x$				$=$	$-$	$2$	$4$

Step 6

Divide each term in $3 x = - 24$ by $3$ and simplify.

Divide each term in $3 x = - 24$ by $3$ .

$\frac{3 x}{3} = \frac{- 24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 24}{3}$

Divide $x$ by $1$ .

$x = \frac{- 24}{3}$

Simplify the right side.

Divide $- 24$ by $3$ .

$x = - 8$

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 $y$ .

$- 4 \cdot - 8 - 6 y = - 10$

Multiply $- 4$ by $- 8$ .

$32 - 6 y = - 10$

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

Subtract $32$ from both sides of the equation.

$- 6 y = - 10 - 32$

Subtract $32$ from $- 10$ .

$- 6 y = - 42$

Divide each term in $- 6 y = - 42$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 42$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 42}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 42}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 42}{- 6}$

Simplify the right side.

Divide $- 42$ by $- 6$ .

$y = 7$

Step 8

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

$(- 8, 7)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 8, 7)$

Equation Form:

$x = - 8, y = 7$

Step 10

Solve by Addition/Elimination 4x-10=-6y , 7x+6y=-14

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