Algebra Examples

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

Step 1

Solve the system of equations.

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Step 1.1

Subtract $x$ from both sides of the equation.

$x - y = - 4, y - x = 4$

Step 1.2

Reorder the polynomial.

$- x + y = 4$

$x - y = - 4$

Step 1.3

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

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

Step 1.4

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

Infinite number of solutions

Step 1.5

Solve one of the equations for $y$ .

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Step 1.5.1

Subtract $x$ from both sides of the equation.

$- y = - 4 - x$

Step 1.5.2

Divide each term in $- y = - 4 - x$ by $- 1$ and simplify.

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Step 1.5.2.1

Divide each term in $- y = - 4 - x$ by $- 1$ .

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

Step 1.5.2.2

Simplify the left side.

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Step 1.5.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.5.2.2.2

Divide $y$ by $1$ .

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

Step 1.5.2.3

Simplify the right side.

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Step 1.5.2.3.1

Simplify each term.

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Step 1.5.2.3.1.1

Divide $- 4$ by $- 1$ .

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

Step 1.5.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.5.2.3.1.3

Divide $x$ by $1$ .

$y = 4 + x$

Step 1.6

The solution is the set of ordered pairs that make $y = 4 + x$ true.

$(x, 4 + x)$

Step 2

Since the system is always true, the equations are equal and the graphs are the same line. Thus, the system is dependent.

Dependent

Step 3