Algebra Examples

$5 x - 9 y = 6$ $- (5 x + 2 y) = (17)$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Simplify $- (5 x + 2 y)$ .

Tap for more steps...

Step 1.1.1

Remove parentheses.

$- (5 x + 2 y) = 17$

$5 x - 9 y = 6$

Step 1.1.2

Apply the distributive property.

$- (5 x) - (2 y) = 17$

$5 x - 9 y = 6$

Step 1.1.3

Multiply.

Tap for more steps...

Step 1.1.3.1

Multiply $5$ by $- 1$ .

$- 5 x - (2 y) = 17$

$5 x - 9 y = 6$

Step 1.1.3.2

Multiply $2$ by $- 1$ .

$- 5 x - 2 y = 17$

$5 x - 9 y = 6$

$- 5 x - 2 y = 17$

$5 x - 9 y = 6$

$- 5 x - 2 y = 17$

$5 x - 9 y = 6$

$- 5 x - 2 y = 17$

$5 x - 9 y = 6$

Step 2

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

		$5$	$x$		$-$	$9$	$y$	$=$		$6$
$+$	$-$	$5$	$x$		$-$	$2$	$y$	$=$	$1$	$7$
				$-$	$1$	$1$	$y$	$=$	$2$	$3$

Step 3

Divide each term in $- 11 y = 23$ by $- 11$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- 11 y = 23$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{23}{- 11}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 11$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{23}{- 11}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{23}{- 11}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move the negative in front of the fraction.

$y = - \frac{23}{11}$

Step 4

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Tap for more steps...

Step 4.1

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$5 x - 9 (- \frac{23}{11}) = 6$

Step 4.2

Multiply $- 9 (- \frac{23}{11})$ .

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $- 9$ .

$5 x + 9 (\frac{23}{11}) = 6$

Step 4.2.2

Combine $9$ and $\frac{23}{11}$ .

$5 x + \frac{9 \cdot 23}{11} = 6$

Step 4.2.3

Multiply $9$ by $23$ .

$5 x + \frac{207}{11} = 6$

Step 4.3

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 4.3.1

Subtract $\frac{207}{11}$ from both sides of the equation.

$5 x = 6 - \frac{207}{11}$

Step 4.3.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$5 x = 6 \cdot \frac{11}{11} - \frac{207}{11}$

Step 4.3.3

Combine $6$ and $\frac{11}{11}$ .

$5 x = \frac{6 \cdot 11}{11} - \frac{207}{11}$

Step 4.3.4

Combine the numerators over the common denominator.

$5 x = \frac{6 \cdot 11 - 207}{11}$

Step 4.3.5

Simplify the numerator.

Tap for more steps...

Step 4.3.5.1

Multiply $6$ by $11$ .

$5 x = \frac{66 - 207}{11}$

Step 4.3.5.2

Subtract $207$ from $66$ .

$5 x = \frac{- 141}{11}$

Step 4.3.6

Move the negative in front of the fraction.

$5 x = - \frac{141}{11}$

Step 4.4

Divide each term in $5 x = - \frac{141}{11}$ by $5$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $5 x = - \frac{141}{11}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{141}{11}}{5}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{141}{11}}{5}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{141}{11}}{5}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{141}{11} \cdot \frac{1}{5}$

Step 4.4.3.2

Multiply $- \frac{141}{11} \cdot \frac{1}{5}$ .

Tap for more steps...

Step 4.4.3.2.1

Multiply $\frac{1}{5}$ by $\frac{141}{11}$ .

$x = - \frac{141}{5 \cdot 11}$

Step 4.4.3.2.2

Multiply $5$ by $11$ .

$x = - \frac{141}{55}$

Step 5

The solution to the independent system of equations can be represented as a point.

$(- \frac{141}{55}, - \frac{23}{11})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{141}{55}, - \frac{23}{11})$

Equation Form:

$x = - \frac{141}{55}, y = - \frac{23}{11}$

Step 7

		$5$	$x$		$-$	$9$	$y$	$=$		$6$
$+$	$-$	$5$	$x$		$-$	$2$	$y$	$=$	$1$	$7$
				$-$	$1$	$1$	$y$	$=$	$2$	$3$

		$5$	$x$		$-$	$9$	$y$	$=$		$6$
$+$	$-$	$5$	$x$		$-$	$2$	$y$	$=$	$1$	$7$
				$-$	$1$	$1$	$y$	$=$	$2$	$3$

		$5$	$x$		$-$	$9$	$y$	$=$		$6$
$+$	$-$	$5$	$x$		$-$	$2$	$y$	$=$	$1$	$7$
				$-$	$1$	$1$	$y$	$=$	$2$	$3$