Solve by Addition/Elimination x/3+(4y)/3=300 3x-4y=300

$\frac{x}{3} + \frac{4 y}{3} = 300$ $3 x - 4 y = 300$

Step 1

Multiply each term in $\frac{x}{3} + \frac{4 y}{3} = 300$ by $3$ to eliminate the fractions.

Multiply each term in $\frac{x}{3} + \frac{4 y}{3} = 300$ by $3$ .

$\frac{x}{3} \cdot 3 + \frac{4 y}{3} \cdot 3 = 300 \cdot 3$

$3 x - 4 y = 300$

Simplify the left side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x}{3} \cdot 3 + \frac{4 y}{3} \cdot 3 = 300 \cdot 3$

$3 x - 4 y = 300$

Rewrite the expression.

$x + \frac{4 y}{3} \cdot 3 = 300 \cdot 3$

$3 x - 4 y = 300$

$x + \frac{4 y}{3} \cdot 3 = 300 \cdot 3$

$3 x - 4 y = 300$

Cancel the common factor of $3$ .

Cancel the common factor.

$x + \frac{4 y}{3} \cdot 3 = 300 \cdot 3$

$3 x - 4 y = 300$

Rewrite the expression.

$x + 4 y = 300 \cdot 3$

$3 x - 4 y = 300$

$x + 4 y = 300 \cdot 3$

$3 x - 4 y = 300$

$x + 4 y = 300 \cdot 3$

$3 x - 4 y = 300$

$x + 4 y = 300 \cdot 3$

$3 x - 4 y = 300$

Simplify the right side.

Multiply $300$ by $3$ .

$x + 4 y = 900$

$3 x - 4 y = 300$

$x + 4 y = 900$

$3 x - 4 y = 300$

$x + 4 y = 900$

$3 x - 4 y = 300$

Step 2

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

$(- 3) \cdot (x + 4 y) = (- 3) (900)$

$3 x - 4 y = 300$

Step 3

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (x + 4 y)$ .

Apply the distributive property.

$- 3 x - 3 (4 y) = (- 3) (900)$

$3 x - 4 y = 300$

Multiply $4$ by $- 3$ .

$- 3 x - 12 y = (- 3) (900)$

$3 x - 4 y = 300$

$- 3 x - 12 y = (- 3) (900)$

$3 x - 4 y = 300$

$- 3 x - 12 y = (- 3) (900)$

$3 x - 4 y = 300$

Simplify the right side.

Multiply $- 3$ by $900$ .

$- 3 x - 12 y = - 2700$

$3 x - 4 y = 300$

$- 3 x - 12 y = - 2700$

$3 x - 4 y = 300$

$- 3 x - 12 y = - 2700$

$3 x - 4 y = 300$

Step 4

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

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

Step 5

Divide each term in $- 16 y = - 2400$ by $- 16$ and simplify.

Divide each term in $- 16 y = - 2400$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{- 2400}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{- 2400}{- 16}$

Divide $y$ by $1$ .

$y = \frac{- 2400}{- 16}$

Simplify the right side.

Divide $- 2400$ by $- 16$ .

$y = 150$

Step 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 $x$ .

$- 3 x - 12 \cdot 150 = - 2700$

Multiply $- 12$ by $150$ .

$- 3 x - 1800 = - 2700$

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

Add $1800$ to both sides of the equation.

$- 3 x = - 2700 + 1800$

Add $- 2700$ and $1800$ .

$- 3 x = - 900$

Divide each term in $- 3 x = - 900$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 900$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 900}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 900}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 900}{- 3}$

Simplify the right side.

Divide $- 900$ by $- 3$ .

$x = 300$

Step 7

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

$(300, 150)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(300, 150)$

Equation Form:

$x = 300, y = 150$

Step 9

Solve by Addition/Elimination x/3+(4y)/3=300 3x-4y=300

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