Algebra Examples

$- x - 2 y = 3$ $x + 2 y = - 3$

Step 1

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

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

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 $x$ to both sides of the equation.

$- 2 y = 3 + x$

Step 3.2

Divide each term in $- 2 y = 3 + x$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 y = 3 + x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{3}{- 2} + \frac{x}{- 2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{3}{- 2} + \frac{x}{- 2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{- 2} + \frac{x}{- 2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{x}{- 2}$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3}{2} - \frac{x}{2}$

Step 4

The solution is the set of ordered pairs that make $y = - \frac{3}{2} - \frac{x}{2}$ true.

$(x, - \frac{3}{2} - \frac{x}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{3}{2} - \frac{x}{2})$

Equation Form:

$x = x, y = - \frac{3}{2} - \frac{x}{2}$

Step 6