Algebra Examples

$3 x - y = 28$ $3 x + y = 14$

Step 1

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

	$3$	$x$	$-$	$y$	$=$	$2$	$8$
$+$	$3$	$x$	$+$	$y$	$=$	$1$	$4$
	$6$	$x$			$=$	$4$	$2$

Step 2

Divide each term in $6 x = 42$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 x = 42$ by $6$ .

$\frac{6 x}{6} = \frac{42}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{42}{6}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{42}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $42$ by $6$ .

$x = 7$

Step 3

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

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Step 3.1

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

$3 (7) - y = 28$

Step 3.2

Multiply $3$ by $7$ .

$21 - y = 28$

Step 3.3

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

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Step 3.3.1

Subtract $21$ from both sides of the equation.

$- y = 28 - 21$

Step 3.3.2

Subtract $21$ from $28$ .

$- y = 7$

Step 3.4

Divide each term in $- y = 7$ by $- 1$ and simplify.

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Step 3.4.1

Divide each term in $- y = 7$ by $- 1$ .

$\frac{- y}{- 1} = \frac{7}{- 1}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{7}{- 1}$

Step 3.4.2.2

Divide $y$ by $1$ .

$y = \frac{7}{- 1}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $7$ by $- 1$ .

$y = - 7$

Step 4

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

$(7, - 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(7, - 7)$

Equation Form:

$x = 7, y = - 7$

Step 6

	$3$	$x$	$-$	$y$	$=$	$2$	$8$
$+$	$3$	$x$	$+$	$y$	$=$	$1$	$4$
	$6$	$x$			$=$	$4$	$2$

	$3$	$x$	$-$	$y$	$=$	$2$	$8$
$+$	$3$	$x$	$+$	$y$	$=$	$1$	$4$
	$6$	$x$			$=$	$4$	$2$

	$3$	$x$	$-$	$y$	$=$	$2$	$8$
$+$	$3$	$x$	$+$	$y$	$=$	$1$	$4$
	$6$	$x$			$=$	$4$	$2$