Solve by Addition/Elimination 10y+7x=29 -5y-9x=2

$10 y + 7 x = 29$ $- 5 y - 9 x = 2$

Simplify the left side.

Reorder $10 y$ and $7 x$ .

$7 x + 10 y = 29$

$- 5 y - 9 x = 2$

$7 x + 10 y = 29$

$- 5 y - 9 x = 2$

Simplify the left side.

Reorder $- 5 y$ and $- 9 x$ .

$- 9 x - 5 y = 2$

$7 x + 10 y = 29$

$- 9 x - 5 y = 2$

$7 x + 10 y = 29$

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

$7 x + 10 y = 29$

$(2) \cdot (- 9 x - 5 y) = (2) (2)$

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 9 x - 5 y)$ .

Apply the distributive property.

$7 x + 10 y = 29$

$2 (- 9 x) + 2 (- 5 y) = (2) (2)$

Multiply.

Multiply $- 9$ by $2$ .

$7 x + 10 y = 29$

$- 18 x + 2 (- 5 y) = (2) (2)$

Multiply $- 5$ by $2$ .

$7 x + 10 y = 29$

$- 18 x - 10 y = (2) (2)$

$7 x + 10 y = 29$

$- 18 x - 10 y = (2) (2)$

$7 x + 10 y = 29$

$- 18 x - 10 y = (2) (2)$

$7 x + 10 y = 29$

$- 18 x - 10 y = (2) (2)$

Simplify the right side.

Multiply $2$ by $2$ .

$7 x + 10 y = 29$

$- 18 x - 10 y = 4$

$7 x + 10 y = 29$

$- 18 x - 10 y = 4$

$7 x + 10 y = 29$

$- 18 x - 10 y = 4$

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

			$7$	$x$	$+$	$1$	$0$	$y$	$=$	$2$	$9$
$+$	$-$	$1$	$8$	$x$	$-$	$1$	$0$	$y$	$=$		$4$
	$-$	$1$	$1$	$x$					$=$	$3$	$3$

Divide each term in $- 11 x = 33$ by $- 11$ and simplify.

Divide each term in $- 11 x = 33$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{33}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{33}{- 11}$

Divide $x$ by $1$ .

$x = \frac{33}{- 11}$

Simplify the right side.

Divide $33$ by $- 11$ .

$x = - 3$

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 $y$ .

$7 (- 3) + 10 y = 29$

Multiply $7$ by $- 3$ .

$- 21 + 10 y = 29$

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

Add $21$ to both sides of the equation.

$10 y = 29 + 21$

Add $29$ and $21$ .

$10 y = 50$

Divide each term in $10 y = 50$ by $10$ and simplify.

Divide each term in $10 y = 50$ by $10$ .

$\frac{10 y}{10} = \frac{50}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{50}{10}$

Divide $y$ by $1$ .

$y = \frac{50}{10}$

Simplify the right side.

Divide $50$ by $10$ .

$y = 5$

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

$(- 3, 5)$

The result can be shown in multiple forms.

Point Form:

$(- 3, 5)$

Equation Form:

$x = - 3, y = 5$

Solve by Addition/Elimination 10y+7x=29 -5y-9x=2

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