Algebra Examples

$- 6 y + 2 = - 4 x$ $y - 2 = x$

Step 1

Move all terms containing variables to the left.

Tap for more steps...

Step 1.1

Subtract $2$ from both sides of the equation.

$- 6 y = - 4 x - 2, y - 2 = x$

Step 1.2

Add $4 x$ to both sides of the equation.

$- 6 y + 4 x = - 2, y - 2 = x$

Step 1.3

Add $2$ to both sides of the equation.

$- 6 y + 4 x = - 2, y = x + 2$

Step 1.4

Subtract $x$ from both sides of the equation.

$- 6 y + 4 x = - 2, y - x = 2$

Step 2

Reorder the polynomial.

$4 x - 6 y = - 2$

$y - x = 2$

Step 3

Reorder the polynomial.

$- x + y = 2$

$4 x - 6 y = - 2$

Step 4

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

$4 x - 6 y = - 2$

$(4) \cdot (- x + y) = (4) (2)$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

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

Tap for more steps...

Step 5.1.1.1

Apply the distributive property.

$4 x - 6 y = - 2$

$4 (- x) + 4 y = (4) (2)$

Step 5.1.1.2

Multiply $- 1$ by $4$ .

$4 x - 6 y = - 2$

$- 4 x + 4 y = (4) (2)$

$4 x - 6 y = - 2$

$- 4 x + 4 y = (4) (2)$

$4 x - 6 y = - 2$

$- 4 x + 4 y = (4) (2)$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $4$ by $2$ .

$4 x - 6 y = - 2$

$- 4 x + 4 y = 8$

$4 x - 6 y = - 2$

$- 4 x + 4 y = 8$

$4 x - 6 y = - 2$

$- 4 x + 4 y = 8$

Step 6

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

		$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$
$+$	$-$	$4$	$x$	$+$	$4$	$y$	$=$		$8$
				$-$	$2$	$y$	$=$		$6$

Step 7

Divide each term in $- 2 y = 6$ by $- 2$ and simplify.

Tap for more steps...

Step 7.1

Divide each term in $- 2 y = 6$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{6}{- 2}$

Step 7.2

Simplify the left side.

Tap for more steps...

Step 7.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{6}{- 2}$

Step 7.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 2}$

Step 7.3

Simplify the right side.

Tap for more steps...

Step 7.3.1

Divide $6$ by $- 2$ .

$y = - 3$

Step 8

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

Tap for more steps...

Step 8.1

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

$4 x - 6 \cdot - 3 = - 2$

Step 8.2

Multiply $- 6$ by $- 3$ .

$4 x + 18 = - 2$

Step 8.3

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

Tap for more steps...

Step 8.3.1

Subtract $18$ from both sides of the equation.

$4 x = - 2 - 18$

Step 8.3.2

Subtract $18$ from $- 2$ .

$4 x = - 20$

Step 8.4

Divide each term in $4 x = - 20$ by $4$ and simplify.

Tap for more steps...

Step 8.4.1

Divide each term in $4 x = - 20$ by $4$ .

$\frac{4 x}{4} = \frac{- 20}{4}$

Step 8.4.2

Simplify the left side.

Tap for more steps...

Step 8.4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 8.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 20}{4}$

Step 8.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 20}{4}$

Step 8.4.3

Simplify the right side.

Tap for more steps...

Step 8.4.3.1

Divide $- 20$ by $4$ .

$x = - 5$

Step 9

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

$(- 5, - 3)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(- 5, - 3)$

Equation Form:

$x = - 5, y = - 3$

Step 11

		$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$
$+$	$-$	$4$	$x$	$+$	$4$	$y$	$=$		$8$
				$-$	$2$	$y$	$=$		$6$

		$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$
$+$	$-$	$4$	$x$	$+$	$4$	$y$	$=$		$8$
				$-$	$2$	$y$	$=$		$6$

		$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$
$+$	$-$	$4$	$x$	$+$	$4$	$y$	$=$		$8$
				$-$	$2$	$y$	$=$		$6$