Algebra Examples

$2 x + 3 y = 6$ $2 y = 5 - x$

Step 1

Simplify the right side.

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Step 1.1

Reorder $5$ and $- x$ .

$2 y = - x + 5$

$2 x + 3 y = 6$

$2 y = - x + 5$

$2 x + 3 y = 6$

Step 2

Add $x$ to both sides of the equation.

$2 x + 3 y = 6, 2 y + x = 5$

Step 3

Reorder the polynomial.

$x + 2 y = 5$

$2 x + 3 y = 6$

Step 4

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

$2 x + 3 y = 6$

$(- 2) \cdot (x + 2 y) = (- 2) (5)$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Apply the distributive property.

$2 x + 3 y = 6$

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

Step 5.1.1.2

Multiply $2$ by $- 2$ .

$2 x + 3 y = 6$

$- 2 x - 4 y = (- 2) (5)$

$2 x + 3 y = 6$

$- 2 x - 4 y = (- 2) (5)$

$2 x + 3 y = 6$

$- 2 x - 4 y = (- 2) (5)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 2$ by $5$ .

$2 x + 3 y = 6$

$- 2 x - 4 y = - 10$

$2 x + 3 y = 6$

$- 2 x - 4 y = - 10$

$2 x + 3 y = 6$

$- 2 x - 4 y = - 10$

Step 6

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

		$2$	$x$	$+$	$3$	$y$	$=$			$6$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$1$	$0$
					$-$	$y$	$=$		$-$	$4$

Step 7

Divide each term in $- y = - 4$ by $- 1$ and simplify.

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Step 7.1

Divide each term in $- y = - 4$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1}$

Step 7.2.2

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 4$ by $- 1$ .

$y = 4$

Step 8

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

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Step 8.1

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

$2 x + 3 (4) = 6$

Step 8.2

Multiply $3$ by $4$ .

$2 x + 12 = 6$

Step 8.3

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

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Step 8.3.1

Subtract $12$ from both sides of the equation.

$2 x = 6 - 12$

Step 8.3.2

Subtract $12$ from $6$ .

$2 x = - 6$

Step 8.4

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

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Step 8.4.1

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

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

Step 8.4.2

Simplify the left side.

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Step 8.4.2.1

Cancel the common factor of $2$ .

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Step 8.4.2.1.1

Cancel the common factor.

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

Step 8.4.2.1.2

Divide $x$ by $1$ .

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

Step 8.4.3

Simplify the right side.

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Step 8.4.3.1

Divide $- 6$ by $2$ .

$x = - 3$

Step 9

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

$(- 3, 4)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(- 3, 4)$

Equation Form:

$x = - 3, y = 4$

Step 11

		$2$	$x$	$+$	$3$	$y$	$=$			$6$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$1$	$0$
					$-$	$y$	$=$		$-$	$4$

		$2$	$x$	$+$	$3$	$y$	$=$			$6$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$1$	$0$
					$-$	$y$	$=$		$-$	$4$

		$2$	$x$	$+$	$3$	$y$	$=$			$6$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$1$	$0$
					$-$	$y$	$=$		$-$	$4$