Algebra Examples

$- 2 x + y = - 8$ $x - \frac{1}{2} y = 4$

Step 1

Multiply each term in $x - \frac{1}{2} y = 4$ by $2$ to eliminate the fractions.

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Step 1.1

Multiply each term in $x - \frac{1}{2} y = 4$ by $2$ .

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

$- 2 x + y = - 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Move $2$ to the left of $x$ .

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

$- 2 x + y = - 8$

Step 1.2.1.2

Combine $y$ and $\frac{1}{2}$ .

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

$- 2 x + y = - 8$

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Move the leading negative in $- \frac{y}{2}$ into the numerator.

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

$- 2 x + y = - 8$

Step 1.2.1.3.2

Cancel the common factor.

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

$- 2 x + y = - 8$

Step 1.2.1.3.3

Rewrite the expression.

$2 x - y = 4 \cdot 2$

$- 2 x + y = - 8$

$2 x - y = 4 \cdot 2$

$- 2 x + y = - 8$

$2 x - y = 4 \cdot 2$

$- 2 x + y = - 8$

$2 x - y = 4 \cdot 2$

$- 2 x + y = - 8$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $4$ by $2$ .

$2 x - y = 8$

$- 2 x + y = - 8$

$2 x - y = 8$

$- 2 x + y = - 8$

$2 x - y = 8$

$- 2 x + y = - 8$

Step 2

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

	$-$	$2$	$x$	$+$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$-$	$y$	$=$		$8$
					$0$	$=$		$0$

Step 3

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

Infinite number of solutions

Step 4

Add $2 x$ to both sides of the equation.

$y = - 8 + 2 x$

Step 5

The solution is the set of ordered pairs that make $y = - 8 + 2 x$ true.

$(x, - 8 + 2 x)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(x, - 8 + 2 x)$

Equation Form:

$x = x, y = - 8 + 2 x$

Step 7