Algebra Examples

$3 x - 30 = y$ $7 y - 6 = 3 x$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Add $30$ to both sides of the equation.

$3 x = y + 30, 7 y - 6 = 3 x$

Step 1.2

Subtract $y$ from both sides of the equation.

$3 x - y = 30, 7 y - 6 = 3 x$

Step 1.3

Add $6$ to both sides of the equation.

$3 x - y = 30, 7 y = 3 x + 6$

Step 1.4

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

$3 x - y = 30, 7 y - 3 x = 6$

Step 2

Reorder the polynomial.

$- 3 x + 7 y = 6$

$3 x - y = 30$

Step 3

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

		$3$	$x$		$-$	$y$	$=$	$3$	$0$
$+$	$-$	$3$	$x$	$+$	$7$	$y$	$=$		$6$
					$6$	$y$	$=$	$3$	$6$

Step 4

Divide each term in $6 y = 36$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 y = 36$ by $6$ .

$\frac{6 y}{6} = \frac{36}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{36}{6}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{36}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $36$ by $6$ .

$y = 6$

Step 5

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

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Step 5.1

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

$3 x - (6) = 30$

Step 5.2

Multiply $- 1$ by $6$ .

$3 x - 6 = 30$

Step 5.3

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

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Step 5.3.1

Add $6$ to both sides of the equation.

$3 x = 30 + 6$

Step 5.3.2

Add $30$ and $6$ .

$3 x = 36$

Step 5.4

Divide each term in $3 x = 36$ by $3$ and simplify.

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Step 5.4.1

Divide each term in $3 x = 36$ by $3$ .

$\frac{3 x}{3} = \frac{36}{3}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $3$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{36}{3}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{3}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $36$ by $3$ .

$x = 12$

Step 6

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

$(12, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(12, 6)$

Equation Form:

$x = 12, y = 6$

Step 8

		$3$	$x$		$-$	$y$	$=$	$3$	$0$
$+$	$-$	$3$	$x$	$+$	$7$	$y$	$=$		$6$
					$6$	$y$	$=$	$3$	$6$

		$3$	$x$		$-$	$y$	$=$	$3$	$0$
$+$	$-$	$3$	$x$	$+$	$7$	$y$	$=$		$6$
					$6$	$y$	$=$	$3$	$6$

		$3$	$x$		$-$	$y$	$=$	$3$	$0$
$+$	$-$	$3$	$x$	$+$	$7$	$y$	$=$		$6$
					$6$	$y$	$=$	$3$	$6$