Solve by Addition/Elimination 5x-2y=3 , 2x-y=0

$5 x - 2 y = 3$ , $2 x - y = 0$

Step 1

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

$5 x - 2 y = 3$

$(- 2) \cdot (2 x - y) = (- 2) (0)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$5 x - 2 y = 3$

$- 2 (2 x) - 2 (- y) = (- 2) (0)$

Multiply.

Multiply $2$ by $- 2$ .

$5 x - 2 y = 3$

$- 4 x - 2 (- y) = (- 2) (0)$

Multiply $- 1$ by $- 2$ .

$5 x - 2 y = 3$

$- 4 x + 2 y = (- 2) (0)$

$5 x - 2 y = 3$

$- 4 x + 2 y = (- 2) (0)$

$5 x - 2 y = 3$

$- 4 x + 2 y = (- 2) (0)$

$5 x - 2 y = 3$

$- 4 x + 2 y = (- 2) (0)$

Simplify the right side.

Multiply $- 2$ by $0$ .

$5 x - 2 y = 3$

$- 4 x + 2 y = 0$

$5 x - 2 y = 3$

$- 4 x + 2 y = 0$

$5 x - 2 y = 3$

$- 4 x + 2 y = 0$

Step 3

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

		$5$	$x$	$-$	$2$	$y$	$=$	$3$
$+$	$-$	$4$	$x$	$+$	$2$	$y$	$=$	$0$
			$x$				$=$	$3$

Step 4

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 $y$ .

$5 (3) - 2 y = 3$

Multiply $5$ by $3$ .

$15 - 2 y = 3$

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

Subtract $15$ from both sides of the equation.

$- 2 y = 3 - 15$

Subtract $15$ from $3$ .

$- 2 y = - 12$

Divide each term in $- 2 y = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 12$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$y = 6$

Step 5

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

$(3, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 6)$

Equation Form:

$x = 3, y = 6$

Step 7

Solve by Addition/Elimination 5x-2y=3 , 2x-y=0

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