Algebra Examples

$7 x - y = 6$ , $- 7 x + y = - 6$

Step 1

Solve the system of equations.

Tap for more steps...

Step 1.1

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

		$7$	$x$	$-$	$y$	$=$		$6$
$+$	$-$	$7$	$x$	$+$	$y$	$=$	$-$	$6$
					$0$	$=$		$0$

Step 1.2

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

Infinite number of solutions

Step 1.3

Solve one of the equations for $y$ .

Tap for more steps...

Step 1.3.1

Subtract $7 x$ from both sides of the equation.

$- y = 6 - 7 x$

Step 1.3.2

Divide each term in $- y = 6 - 7 x$ by $- 1$ and simplify.

Tap for more steps...

Step 1.3.2.1

Divide each term in $- y = 6 - 7 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- 7 x}{- 1}$

Step 1.3.2.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- 7 x}{- 1}$

Step 1.3.2.2.2

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{- 7 x}{- 1}$

Step 1.3.2.3

Simplify the right side.

Tap for more steps...

Step 1.3.2.3.1

Simplify each term.

Tap for more steps...

Step 1.3.2.3.1.1

Divide $6$ by $- 1$ .

$y = - 6 + \frac{- 7 x}{- 1}$

Step 1.3.2.3.1.2

Move the negative one from the denominator of $\frac{- 7 x}{- 1}$ .

$y = - 6 - 1 \cdot (- 7 x)$

Step 1.3.2.3.1.3

Rewrite $- 1 \cdot (- 7 x)$ as $- (- 7 x)$ .

$y = - 6 - (- 7 x)$

Step 1.3.2.3.1.4

Multiply $- 7$ by $- 1$ .

$y = - 6 + 7 x$

Step 1.4

The solution is the set of ordered pairs that make $y = - 6 + 7 x$ true.

$(x, - 6 + 7 x)$

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