Algebra Examples

$4 x = 2 y + 18$ $x - 8 y = 12$

Step 1

Subtract $2 y$ from both sides of the equation.

$4 x - 2 y = 18, x - 8 y = 12$

Step 2

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$4 x - 2 y = 18$

$(- 4) \cdot (x - 8 y) = (- 4) (12)$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $(- 4) \cdot (x - 8 y)$ .

Tap for more steps...

Step 3.1.1.1

Apply the distributive property.

$4 x - 2 y = 18$

$- 4 x - 4 (- 8 y) = (- 4) (12)$

Step 3.1.1.2

Multiply $- 8$ by $- 4$ .

$4 x - 2 y = 18$

$- 4 x + 32 y = (- 4) (12)$

$4 x - 2 y = 18$

$- 4 x + 32 y = (- 4) (12)$

$4 x - 2 y = 18$

$- 4 x + 32 y = (- 4) (12)$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 4$ by $12$ .

$4 x - 2 y = 18$

$- 4 x + 32 y = - 48$

$4 x - 2 y = 18$

$- 4 x + 32 y = - 48$

$4 x - 2 y = 18$

$- 4 x + 32 y = - 48$

Step 4

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

		$4$	$x$		$-$	$2$	$y$	$=$		$1$	$8$
$+$	$-$	$4$	$x$	$+$	$3$	$2$	$y$	$=$	$-$	$4$	$8$
					$3$	$0$	$y$	$=$	$-$	$3$	$0$

Step 5

Divide each term in $30 y = - 30$ by $30$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $30 y = - 30$ by $30$ .

$\frac{30 y}{30} = \frac{- 30}{30}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $30$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{30 y}{30} = \frac{- 30}{30}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 30}{30}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $- 30$ by $30$ .

$y = - 1$

Step 6

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

Tap for more steps...

Step 6.1

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

$4 x - 2 \cdot - 1 = 18$

Step 6.2

Multiply $- 2$ by $- 1$ .

$4 x + 2 = 18$

Step 6.3

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

Tap for more steps...

Step 6.3.1

Subtract $2$ from both sides of the equation.

$4 x = 18 - 2$

Step 6.3.2

Subtract $2$ from $18$ .

$4 x = 16$

Step 6.4

Divide each term in $4 x = 16$ by $4$ and simplify.

Tap for more steps...

Step 6.4.1

Divide each term in $4 x = 16$ by $4$ .

$\frac{4 x}{4} = \frac{16}{4}$

Step 6.4.2

Simplify the left side.

Tap for more steps...

Step 6.4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{16}{4}$

Step 6.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{4}$

Step 6.4.3

Simplify the right side.

Tap for more steps...

Step 6.4.3.1

Divide $16$ by $4$ .

$x = 4$

Step 7

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

$(4, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 9

		$4$	$x$		$-$	$2$	$y$	$=$		$1$	$8$
$+$	$-$	$4$	$x$	$+$	$3$	$2$	$y$	$=$	$-$	$4$	$8$
					$3$	$0$	$y$	$=$	$-$	$3$	$0$

		$4$	$x$		$-$	$2$	$y$	$=$		$1$	$8$
$+$	$-$	$4$	$x$	$+$	$3$	$2$	$y$	$=$	$-$	$4$	$8$
					$3$	$0$	$y$	$=$	$-$	$3$	$0$

		$4$	$x$		$-$	$2$	$y$	$=$		$1$	$8$
$+$	$-$	$4$	$x$	$+$	$3$	$2$	$y$	$=$	$-$	$4$	$8$
					$3$	$0$	$y$	$=$	$-$	$3$	$0$