Algebra Examples

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

Step 1

Subtract $y$ from both sides of the equation.

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

Step 2

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

$(2) \cdot (5 x - y) = (2) (6)$

$5 x + 2 y = 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(2) \cdot (5 x - y)$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (5 x) + 2 (- y) = (2) (6)$

$5 x + 2 y = 3$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $5$ by $2$ .

$10 x + 2 (- y) = (2) (6)$

$5 x + 2 y = 3$

Step 3.1.1.2.2

Multiply $- 1$ by $2$ .

$10 x - 2 y = (2) (6)$

$5 x + 2 y = 3$

$10 x - 2 y = (2) (6)$

$5 x + 2 y = 3$

$10 x - 2 y = (2) (6)$

$5 x + 2 y = 3$

$10 x - 2 y = (2) (6)$

$5 x + 2 y = 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $6$ .

$10 x - 2 y = 12$

$5 x + 2 y = 3$

$10 x - 2 y = 12$

$5 x + 2 y = 3$

$10 x - 2 y = 12$

$5 x + 2 y = 3$

Step 4

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

	$1$	$0$	$x$	$-$	$2$	$y$	$=$	$1$	$2$
$+$		$5$	$x$	$+$	$2$	$y$	$=$		$3$
	$1$	$5$	$x$				$=$	$1$	$5$

Step 5

Divide each term in $15 x = 15$ by $15$ and simplify.

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Step 5.1

Divide each term in $15 x = 15$ by $15$ .

$\frac{15 x}{15} = \frac{15}{15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{15 x}{15} = \frac{15}{15}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{15}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $15$ by $15$ .

$x = 1$

Step 6

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

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Step 6.1

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

$10 (1) - 2 y = 12$

Step 6.2

Multiply $10$ by $1$ .

$10 - 2 y = 12$

Step 6.3

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

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Step 6.3.1

Subtract $10$ from both sides of the equation.

$- 2 y = 12 - 10$

Step 6.3.2

Subtract $10$ from $12$ .

$- 2 y = 2$

Step 6.4

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

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Step 6.4.1

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

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

Step 6.4.2

Simplify the left side.

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Step 6.4.2.1

Cancel the common factor of $- 2$ .

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Step 6.4.2.1.1

Cancel the common factor.

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

Step 6.4.2.1.2

Divide $y$ by $1$ .

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

Step 6.4.3

Simplify the right side.

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Step 6.4.3.1

Divide $2$ by $- 2$ .

$y = - 1$

Step 7

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

$(1, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, - 1)$

Equation Form:

$x = 1, y = - 1$

Step 9

	$1$	$0$	$x$	$-$	$2$	$y$	$=$	$1$	$2$
$+$		$5$	$x$	$+$	$2$	$y$	$=$		$3$
	$1$	$5$	$x$				$=$	$1$	$5$

	$1$	$0$	$x$	$-$	$2$	$y$	$=$	$1$	$2$
$+$		$5$	$x$	$+$	$2$	$y$	$=$		$3$
	$1$	$5$	$x$				$=$	$1$	$5$

	$1$	$0$	$x$	$-$	$2$	$y$	$=$	$1$	$2$
$+$		$5$	$x$	$+$	$2$	$y$	$=$		$3$
	$1$	$5$	$x$				$=$	$1$	$5$