Solve by Addition/Elimination 4x-4y=10 , 3x+2y=5

$4 x - 4 y = 10$ , $3 x + 2 y = 5$

Step 1

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

$4 x - 4 y = 10$

$(2) \cdot (3 x + 2 y) = (2) (5)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (3 x + 2 y)$ .

Apply the distributive property.

$4 x - 4 y = 10$

$2 (3 x) + 2 (2 y) = (2) (5)$

Multiply.

Multiply $3$ by $2$ .

$4 x - 4 y = 10$

$6 x + 2 (2 y) = (2) (5)$

Multiply $2$ by $2$ .

$4 x - 4 y = 10$

$6 x + 4 y = (2) (5)$

$4 x - 4 y = 10$

$6 x + 4 y = (2) (5)$

$4 x - 4 y = 10$

$6 x + 4 y = (2) (5)$

$4 x - 4 y = 10$

$6 x + 4 y = (2) (5)$

Simplify the right side.

Multiply $2$ by $5$ .

$4 x - 4 y = 10$

$6 x + 4 y = 10$

$4 x - 4 y = 10$

$6 x + 4 y = 10$

$4 x - 4 y = 10$

$6 x + 4 y = 10$

Step 3

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

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

Step 4

Divide each term in $10 x = 20$ by $10$ and simplify.

Divide each term in $10 x = 20$ by $10$ .

$\frac{10 x}{10} = \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{20}{10}$

Divide $x$ by $1$ .

$x = \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$x = 2$

Step 5

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 $y$ .

$4 (2) - 4 y = 10$

Multiply $4$ by $2$ .

$8 - 4 y = 10$

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

Subtract $8$ from both sides of the equation.

$- 4 y = 10 - 8$

Subtract $8$ from $10$ .

$- 4 y = 2$

Divide each term in $- 4 y = 2$ by $- 4$ and simplify.

Divide each term in $- 4 y = 2$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4}$

Divide $y$ by $1$ .

$y = \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2}$

Rewrite the expression.

$y = \frac{1}{- 2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 6

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

$(2, - \frac{1}{2})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - \frac{1}{2})$

Equation Form:

$x = 2, y = - \frac{1}{2}$

Step 8

Solve by Addition/Elimination 4x-4y=10 , 3x+2y=5

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