Solve by Addition/Elimination 2x-y=1 , 4x-2y=2

$2 x - y = 1$ , $4 x - 2 y = 2$

Step 1

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

$(- 2) \cdot (2 x - y) = (- 2) (1)$

$4 x - 2 y = 2$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 (2 x) - 2 (- y) = (- 2) (1)$

$4 x - 2 y = 2$

Multiply.

Multiply $2$ by $- 2$ .

$- 4 x - 2 (- y) = (- 2) (1)$

$4 x - 2 y = 2$

Multiply $- 1$ by $- 2$ .

$- 4 x + 2 y = (- 2) (1)$

$4 x - 2 y = 2$

$- 4 x + 2 y = (- 2) (1)$

$4 x - 2 y = 2$

$- 4 x + 2 y = (- 2) (1)$

$4 x - 2 y = 2$

$- 4 x + 2 y = (- 2) (1)$

$4 x - 2 y = 2$

Simplify the right side.

Multiply $- 2$ by $1$ .

$- 4 x + 2 y = - 2$

$4 x - 2 y = 2$

$- 4 x + 2 y = - 2$

$4 x - 2 y = 2$

$- 4 x + 2 y = - 2$

$4 x - 2 y = 2$

Step 3

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

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

Step 4

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 5

Solve one of the equations for $y$ .

Add $4 x$ to both sides of the equation.

$2 y = - 2 + 4 x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

$y = - 1 + \frac{4 x}{2}$

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

Factor $2$ out of $4 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

$y = - 1 + \frac{2 (2 x)}{2 \cdot 1}$

Rewrite the expression.

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

Divide $2 x$ by $1$ .

$y = - 1 + 2 x$

Step 6

The solution is the set of ordered pairs that make $y = - 1 + 2 x$ true.

$(x, - 1 + 2 x)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - 1 + 2 x)$

Equation Form:

$x = x, y = - 1 + 2 x$

Step 8

Solve by Addition/Elimination 2x-y=1 , 4x-2y=2

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