Algebra Examples

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

Step 1

Solve the system of equations.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Reorder $y$ and $4 x$ .

$4 x + y = 3$

$4 x = 2 y - 6$

$4 x + y = 3$

$4 x = 2 y - 6$

Step 1.2

Subtract $2 y$ from both sides of the equation.

$4 x - 2 y = - 6, 4 x + y = 3$

Step 1.3

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

$4 x - 2 y = - 6$

$(2) \cdot (4 x + y) = (2) (3)$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $(2) \cdot (4 x + y)$ .

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Step 1.4.1.1.1

Apply the distributive property.

$4 x - 2 y = - 6$

$2 (4 x) + 2 y = (2) (3)$

Step 1.4.1.1.2

Multiply $4$ by $2$ .

$4 x - 2 y = - 6$

$8 x + 2 y = (2) (3)$

$4 x - 2 y = - 6$

$8 x + 2 y = (2) (3)$

$4 x - 2 y = - 6$

$8 x + 2 y = (2) (3)$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $2$ by $3$ .

$4 x - 2 y = - 6$

$8 x + 2 y = 6$

$4 x - 2 y = - 6$

$8 x + 2 y = 6$

$4 x - 2 y = - 6$

$8 x + 2 y = 6$

Step 1.5

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

		$4$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$8$	$x$	$+$	$2$	$y$	$=$		$6$
	$1$	$2$	$x$				$=$		$0$

Step 1.6

Divide each term in $12 x = 0$ by $12$ and simplify.

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Step 1.6.1

Divide each term in $12 x = 0$ by $12$ .

$\frac{12 x}{12} = \frac{0}{12}$

Step 1.6.2

Simplify the left side.

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Step 1.6.2.1

Cancel the common factor of $12$ .

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Step 1.6.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{0}{12}$

Step 1.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{12}$

Step 1.6.3

Simplify the right side.

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Step 1.6.3.1

Divide $0$ by $12$ .

$x = 0$

Step 1.7

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

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Step 1.7.1

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

$4 (0) - 2 y = - 6$

Step 1.7.2

Simplify $4 (0) - 2 y$ .

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Step 1.7.2.1

Multiply $4$ by $0$ .

$0 - 2 y = - 6$

Step 1.7.2.2

Subtract $2 y$ from $0$ .

$- 2 y = - 6$

Step 1.7.3

Divide each term in $- 2 y = - 6$ by $- 2$ and simplify.

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Step 1.7.3.1

Divide each term in $- 2 y = - 6$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

Step 1.7.3.2

Simplify the left side.

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Step 1.7.3.2.1

Cancel the common factor of $- 2$ .

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Step 1.7.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

Step 1.7.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6}{- 2}$

Step 1.7.3.3

Simplify the right side.

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Step 1.7.3.3.1

Divide $- 6$ by $- 2$ .

$y = 3$

Step 1.8

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

$(0, 3)$

Step 2

Since the system has a point of intersection, the system is independent.

Independent

Step 3

		$4$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$8$	$x$	$+$	$2$	$y$	$=$		$6$
	$1$	$2$	$x$				$=$		$0$

		$4$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$8$	$x$	$+$	$2$	$y$	$=$		$6$
	$1$	$2$	$x$				$=$		$0$

		$4$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$8$	$x$	$+$	$2$	$y$	$=$		$6$
	$1$	$2$	$x$				$=$		$0$