Solve by Addition/Elimination 3+2x-y=0 , -3-7y=10x

$3 + 2 x - y = 0$ , $- 3 - 7 y = 10 x$

Step 1

Simplify the left side.

Move $3$ .

$2 x - y + 3 = 0$

$- 3 - 7 y = 10 x$

$2 x - y + 3 = 0$

$- 3 - 7 y = 10 x$

Step 2

Simplify the left side.

Reorder $- 3$ and $- 7 y$ .

$- 7 y - 3 = 10 x$

$2 x - y + 3 = 0$

$- 7 y - 3 = 10 x$

$2 x - y + 3 = 0$

Step 3

Move all terms containing variables to the left.

Subtract $3$ from both sides of the equation.

$2 x - y = - 3, - 7 y - 3 = 10 x$

Add $3$ to both sides of the equation.

$2 x - y = - 3, - 7 y = 10 x + 3$

Subtract $10 x$ from both sides of the equation.

$2 x - y = - 3, - 7 y - 10 x = 3$

Step 4

Reorder the polynomial.

$- 10 x - 7 y = 3$

$2 x - y = - 3$

Step 5

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

$(- 7) \cdot (2 x - y) = (- 7) (- 3)$

$- 10 x - 7 y = 3$

Step 6

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 7 (2 x) - 7 (- y) = (- 7) (- 3)$

$- 10 x - 7 y = 3$

Multiply.

Multiply $2$ by $- 7$ .

$- 14 x - 7 (- y) = (- 7) (- 3)$

$- 10 x - 7 y = 3$

Multiply $- 1$ by $- 7$ .

$- 14 x + 7 y = (- 7) (- 3)$

$- 10 x - 7 y = 3$

$- 14 x + 7 y = (- 7) (- 3)$

$- 10 x - 7 y = 3$

$- 14 x + 7 y = (- 7) (- 3)$

$- 10 x - 7 y = 3$

$- 14 x + 7 y = (- 7) (- 3)$

$- 10 x - 7 y = 3$

Simplify the right side.

Multiply $- 7$ by $- 3$ .

$- 14 x + 7 y = 21$

$- 10 x - 7 y = 3$

$- 14 x + 7 y = 21$

$- 10 x - 7 y = 3$

$- 14 x + 7 y = 21$

$- 10 x - 7 y = 3$

Step 7

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

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

Step 8

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

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

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

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $24$ by $- 24$ .

$x = - 1$

Step 9

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 $y$ .

$- 14 \cdot - 1 + 7 y = 21$

Multiply $- 14$ by $- 1$ .

$14 + 7 y = 21$

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

Subtract $14$ from both sides of the equation.

$7 y = 21 - 14$

Subtract $14$ from $21$ .

$7 y = 7$

Divide each term in $7 y = 7$ by $7$ and simplify.

Divide each term in $7 y = 7$ by $7$ .

$\frac{7 y}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{7}{7}$

Divide $y$ by $1$ .

$y = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$y = 1$

Step 10

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

$(- 1, 1)$

Step 11

The result can be shown in multiple forms.

Point Form:

$(- 1, 1)$

Equation Form:

$x = - 1, y = 1$

Step 12

Solve by Addition/Elimination 3+2x-y=0 , -3-7y=10x

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