Algebra Examples

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

Step 1

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

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

Step 2

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

Infinite number of solutions

Step 3

Solve one of the equations for $y$ .

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Step 3.1

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

$- 4 y = 4 x$

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

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

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Step 3.2.3.1.1

Factor $4$ out of $4 x$ .

$y = \frac{4 (x)}{- 4}$

Step 3.2.3.1.2

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y = - 1 \cdot x$

Step 3.2.3.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y = - x$

Step 4

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

$(x, - x)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(x, - x)$

Equation Form:

$x = x, y = - x$

Step 6