Algebra Examples

$4 x + 2 y = 6$ $- 3 x - 2 y = - 4$

Step 1

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

		$4$	$x$	$+$	$2$	$y$	$=$		$6$
$+$	$-$	$3$	$x$	$-$	$2$	$y$	$=$	$-$	$4$
			$x$				$=$		$2$

Step 2

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

Tap for more steps...

Step 2.1

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

$4 (2) + 2 y = 6$

Step 2.2

Multiply $4$ by $2$ .

$8 + 2 y = 6$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Subtract $8$ from both sides of the equation.

$2 y = 6 - 8$

Step 2.3.2

Subtract $8$ from $6$ .

$2 y = - 2$

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

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

Step 2.4.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor.

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

Step 2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.3

Simplify the right side.

Tap for more steps...

Step 2.4.3.1

Divide $- 2$ by $2$ .

$y = - 1$

Step 3

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

$(2, - 1)$

Step 4

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 5

		$4$	$x$	$+$	$2$	$y$	$=$		$6$
$+$	$-$	$3$	$x$	$-$	$2$	$y$	$=$	$-$	$4$
			$x$				$=$		$2$

		$4$	$x$	$+$	$2$	$y$	$=$		$6$
$+$	$-$	$3$	$x$	$-$	$2$	$y$	$=$	$-$	$4$
			$x$				$=$		$2$

		$4$	$x$	$+$	$2$	$y$	$=$		$6$
$+$	$-$	$3$	$x$	$-$	$2$	$y$	$=$	$-$	$4$
			$x$				$=$		$2$