Solve by Addition/Elimination y=0.30m+30 y=0.10m+90

$y = 0.3 m + 30$ $y = 0.1 m + 90$

Step 1

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

Subtract $0.3 m$ from both sides of the equation.

$y - 0.3 m = 30$

$y = 0.1 m + 90$

Reorder $y$ and $- 0.3 m$ .

$- 0.3 m + y = 30$

$y = 0.1 m + 90$

$- 0.3 m + y = 30$

$y = 0.1 m + 90$

Step 2

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

Subtract $0.1 m$ from both sides of the equation.

$y - 0.1 m = 90$

$- 0.3 m + y = 30$

Reorder $y$ and $- 0.1 m$ .

$- 0.1 m + y = 90$

$- 0.3 m + y = 30$

$- 0.1 m + y = 90$

$- 0.3 m + y = 30$

Step 3

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

$- 0.3 m + y = 30$

$(- 3) \cdot (- 0.1 m + y) = (- 3) (90)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (- 0.1 m + y)$ .

Apply the distributive property.

$- 0.3 m + y = 30$

$- 3 (- 0.1 m) - 3 y = (- 3) (90)$

Multiply $- 0.1$ by $- 3$ .

$- 0.3 m + y = 30$

$0.3 m - 3 y = (- 3) (90)$

$- 0.3 m + y = 30$

$0.3 m - 3 y = (- 3) (90)$

$- 0.3 m + y = 30$

$0.3 m - 3 y = (- 3) (90)$

Simplify the right side.

Multiply $- 3$ by $90$ .

$- 0.3 m + y = 30$

$0.3 m - 3 y = - 270$

$- 0.3 m + y = 30$

$0.3 m - 3 y = - 270$

$- 0.3 m + y = 30$

$0.3 m - 3 y = - 270$

Step 5

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

	$-$	$0$	$.$	$3$	$0$	$m$	$+$		$y$	$=$			$3$	$0$
$+$		$0$	$.$	$3$	$0$	$m$	$-$	$3$	$y$	$=$	$-$	$2$	$7$	$0$
							$-$	$2$	$y$	$=$	$-$	$2$	$4$	$0$

Step 6

Divide each term in $- 2 y = - 240$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 240$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 240}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 240}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 240}{- 2}$

Simplify the right side.

Divide $- 240$ by $- 2$ .

$y = 120$

Step 7

Substitute the value found for $y$ into one of the original equations, then solve for $m$ .

Substitute the value found for $y$ into one of the original equations to solve for $m$ .

$- 0.3 m + 120 = 30$

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

Subtract $120$ from both sides of the equation.

$- 0.3 m = 30 - 120$

Subtract $120$ from $30$ .

$- 0.3 m = - 90$

Divide each term in $- 0.3 m = - 90$ by $- 0.3$ and simplify.

Divide each term in $- 0.3 m = - 90$ by $- 0.3$ .

$\frac{- 0.3 m}{- 0.3} = \frac{- 90}{- 0.3}$

Simplify the left side.

Cancel the common factor of $- 0.3$ .

Cancel the common factor.

$\frac{- 0.3 m}{- 0.3} = \frac{- 90}{- 0.3}$

Divide $m$ by $1$ .

$m = \frac{- 90}{- 0.3}$

Simplify the right side.

Divide $- 90$ by $- 0.3$ .

$m = 300$

Step 8

This is the final solution to the independent system of equations.

$y = 120$

$m = 300$

Solve by Addition/Elimination y=0.30m+30 y=0.10m+90

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