Precalculus Examples

$2 x + y = 4$ , $3 x - y = 14$

Step 1

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

	$2$	$x$	$+$	$y$	$=$		$4$
$+$	$3$	$x$	$-$	$y$	$=$	$1$	$4$
	$5$	$x$			$=$	$1$	$8$

Step 2

Divide each term in $5 x = 18$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x = 18$ by $5$ .

$\frac{5 x}{5} = \frac{18}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{18}{5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{5}$

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 $y$ .

$2 (\frac{18}{5}) + y = 4$

Step 3.2

Multiply $2 (\frac{18}{5})$ .

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Step 3.2.1

Combine $2$ and $\frac{18}{5}$ .

$\frac{2 \cdot 18}{5} + y = 4$

Step 3.2.2

Multiply $2$ by $18$ .

$\frac{36}{5} + y = 4$

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 $\frac{36}{5}$ from both sides of the equation.

$y = 4 - \frac{36}{5}$

Step 3.3.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 4 \cdot \frac{5}{5} - \frac{36}{5}$

Step 3.3.3

Combine $4$ and $\frac{5}{5}$ .

$y = \frac{4 \cdot 5}{5} - \frac{36}{5}$

Step 3.3.4

Combine the numerators over the common denominator.

$y = \frac{4 \cdot 5 - 36}{5}$

Step 3.3.5

Simplify the numerator.

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Step 3.3.5.1

Multiply $4$ by $5$ .

$y = \frac{20 - 36}{5}$

Step 3.3.5.2

Subtract $36$ from $20$ .

$y = \frac{- 16}{5}$

Step 3.3.6

Move the negative in front of the fraction.

$y = - \frac{16}{5}$

Step 4

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

$(\frac{18}{5}, - \frac{16}{5})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{18}{5}, - \frac{16}{5})$

Equation Form:

$x = \frac{18}{5}, y = - \frac{16}{5}$

Step 6