Algebra Examples

$3 x + 3 = 3 y$ $2 x - 6 y = 2$

Step 1

Move all terms containing variables to the left.

Tap for more steps...

Step 1.1

Subtract $3$ from both sides of the equation.

$3 x = 3 y - 3, 2 x - 6 y = 2$

Step 1.2

Subtract $3 y$ from both sides of the equation.

$3 x - 3 y = - 3, 2 x - 6 y = 2$

Step 2

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

$(- 2) \cdot (3 x - 3 y) = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $(- 2) \cdot (3 x - 3 y)$ .

Tap for more steps...

Step 3.1.1.1

Apply the distributive property.

$- 2 (3 x) - 2 (- 3 y) = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 3 y) = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

Step 3.1.1.2.2

Multiply $- 3$ by $- 2$ .

$- 6 x + 6 y = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

$- 6 x + 6 y = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

$- 6 x + 6 y = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

$- 6 x + 6 y = (- 2) (- 3)$

$(3) \cdot (2 x - 6 y) = (3) (2)$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 2$ by $- 3$ .

$- 6 x + 6 y = 6$

$(3) \cdot (2 x - 6 y) = (3) (2)$

$- 6 x + 6 y = 6$

$(3) \cdot (2 x - 6 y) = (3) (2)$

Step 3.3

Simplify the left side.

Tap for more steps...

Step 3.3.1

Simplify $(3) \cdot (2 x - 6 y)$ .

Tap for more steps...

Step 3.3.1.1

Apply the distributive property.

$- 6 x + 6 y = 6$

$3 (2 x) + 3 (- 6 y) = (3) (2)$

Step 3.3.1.2

Multiply.

Tap for more steps...

Step 3.3.1.2.1

Multiply $2$ by $3$ .

$- 6 x + 6 y = 6$

$6 x + 3 (- 6 y) = (3) (2)$

Step 3.3.1.2.2

Multiply $- 6$ by $3$ .

$- 6 x + 6 y = 6$

$6 x - 18 y = (3) (2)$

$- 6 x + 6 y = 6$

$6 x - 18 y = (3) (2)$

$- 6 x + 6 y = 6$

$6 x - 18 y = (3) (2)$

$- 6 x + 6 y = 6$

$6 x - 18 y = (3) (2)$

Step 3.4

Simplify the right side.

Tap for more steps...

Step 3.4.1

Multiply $3$ by $2$ .

$- 6 x + 6 y = 6$

$6 x - 18 y = 6$

$- 6 x + 6 y = 6$

$6 x - 18 y = 6$

$- 6 x + 6 y = 6$

$6 x - 18 y = 6$

Step 4

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

	$-$	$6$	$x$	$+$		$6$	$y$	$=$	$6$
$+$		$6$	$x$	$-$	$1$	$8$	$y$	$=$	$6$
				$-$	$1$	$2$	$y$	$=$	$1$	$2$

Step 5

Divide each term in $- 12 y = 12$ by $- 12$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 12 y = 12$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{12}{- 12}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 12$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{12}{- 12}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 12}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $12$ by $- 12$ .

$y = - 1$

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 $x$ .

$- 6 x + 6 (- 1) = 6$

Step 6.2

Multiply $6$ by $- 1$ .

$- 6 x - 6 = 6$

Step 6.3

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

Tap for more steps...

Step 6.3.1

Add $6$ to both sides of the equation.

$- 6 x = 6 + 6$

Step 6.3.2

Add $6$ and $6$ .

$- 6 x = 12$

Step 6.4

Divide each term in $- 6 x = 12$ by $- 6$ and simplify.

Tap for more steps...

Step 6.4.1

Divide each term in $- 6 x = 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{12}{- 6}$

Step 6.4.2

Simplify the left side.

Tap for more steps...

Step 6.4.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 6.4.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{12}{- 6}$

Step 6.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{- 6}$

Step 6.4.3

Simplify the right side.

Tap for more steps...

Step 6.4.3.1

Divide $12$ by $- 6$ .

$x = - 2$

Step 7

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

$(- 2, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1)$

Equation Form:

$x = - 2, y = - 1$

Step 9

	$-$	$6$	$x$	$+$		$6$	$y$	$=$	$6$
$+$		$6$	$x$	$-$	$1$	$8$	$y$	$=$	$6$
				$-$	$1$	$2$	$y$	$=$	$1$	$2$

	$-$	$6$	$x$	$+$		$6$	$y$	$=$	$6$
$+$		$6$	$x$	$-$	$1$	$8$	$y$	$=$	$6$
				$-$	$1$	$2$	$y$	$=$	$1$	$2$

	$-$	$6$	$x$	$+$		$6$	$y$	$=$	$6$
$+$		$6$	$x$	$-$	$1$	$8$	$y$	$=$	$6$
				$-$	$1$	$2$	$y$	$=$	$1$	$2$