Algebra Examples

$y = - 3 x + 5$ $y = - 8 x + 25$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Add $3 x$ to both sides of the equation.

$y + 3 x = 5, y = - 8 x + 25$

Step 1.2

Add $8 x$ to both sides of the equation.

$y + 3 x = 5, y + 8 x = 25$

Step 2

Reorder the polynomial.

$3 x + y = 5$

$y + 8 x = 25$

Step 3

Reorder the polynomial.

$8 x + y = 25$

$3 x + y = 5$

Step 4

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

$3 x + y = 5$

$(- 1) \cdot (8 x + y) = (- 1) (25)$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $(- 1) \cdot (8 x + y)$ .

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Step 5.1.1.1

Apply the distributive property.

$3 x + y = 5$

$- 1 (8 x) - 1 y = (- 1) (25)$

Step 5.1.1.2

Simplify the expression.

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Step 5.1.1.2.1

Multiply $8$ by $- 1$ .

$3 x + y = 5$

$- 8 x - 1 y = (- 1) (25)$

Step 5.1.1.2.2

Rewrite $- 1 y$ as $- y$ .

$3 x + y = 5$

$- 8 x - y = (- 1) (25)$

$3 x + y = 5$

$- 8 x - y = (- 1) (25)$

$3 x + y = 5$

$- 8 x - y = (- 1) (25)$

$3 x + y = 5$

$- 8 x - y = (- 1) (25)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 1$ by $25$ .

$3 x + y = 5$

$- 8 x - y = - 25$

$3 x + y = 5$

$- 8 x - y = - 25$

$3 x + y = 5$

$- 8 x - y = - 25$

Step 6

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

		$3$	$x$	$+$	$y$	$=$			$5$
$+$	$-$	$8$	$x$	$-$	$y$	$=$	$-$	$2$	$5$
	$-$	$5$	$x$			$=$	$-$	$2$	$0$

Step 7

Divide each term in $- 5 x = - 20$ by $- 5$ and simplify.

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Step 7.1

Divide each term in $- 5 x = - 20$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 20}{- 5}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 5$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 20}{- 5}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 20}{- 5}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 20$ by $- 5$ .

$x = 4$

Step 8

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

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Step 8.1

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

$3 (4) + y = 5$

Step 8.2

Multiply $3$ by $4$ .

$12 + y = 5$

Step 8.3

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

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Step 8.3.1

Subtract $12$ from both sides of the equation.

$y = 5 - 12$

Step 8.3.2

Subtract $12$ from $5$ .

$y = - 7$

Step 9

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

$(4, - 7)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(4, - 7)$

Equation Form:

$x = 4, y = - 7$

Step 11

		$3$	$x$	$+$	$y$	$=$			$5$
$+$	$-$	$8$	$x$	$-$	$y$	$=$	$-$	$2$	$5$
	$-$	$5$	$x$			$=$	$-$	$2$	$0$

		$3$	$x$	$+$	$y$	$=$			$5$
$+$	$-$	$8$	$x$	$-$	$y$	$=$	$-$	$2$	$5$
	$-$	$5$	$x$			$=$	$-$	$2$	$0$

		$3$	$x$	$+$	$y$	$=$			$5$
$+$	$-$	$8$	$x$	$-$	$y$	$=$	$-$	$2$	$5$
	$-$	$5$	$x$			$=$	$-$	$2$	$0$