Algebra Examples

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

Step 1

Solve the system of equations.

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Step 1.1

Move all terms containing variables to the left.

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Step 1.1.1

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

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

Step 1.1.2

Subtract $4$ from both sides of the equation.

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

Step 1.1.3

Subtract $y$ from both sides of the equation.

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

Step 1.2

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

$4 x - 2 y = - 6$

$(- 2) \cdot (2 x - y) = (- 2) (- 4)$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $(- 2) \cdot (2 x - y)$ .

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Step 1.3.1.1.1

Apply the distributive property.

$4 x - 2 y = - 6$

$- 2 (2 x) - 2 (- y) = (- 2) (- 4)$

Step 1.3.1.1.2

Multiply.

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Step 1.3.1.1.2.1

Multiply $2$ by $- 2$ .

$4 x - 2 y = - 6$

$- 4 x - 2 (- y) = (- 2) (- 4)$

Step 1.3.1.1.2.2

Multiply $- 1$ by $- 2$ .

$4 x - 2 y = - 6$

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

$4 x - 2 y = - 6$

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

$4 x - 2 y = - 6$

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

$4 x - 2 y = - 6$

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

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $- 2$ by $- 4$ .

$4 x - 2 y = - 6$

$- 4 x + 2 y = 8$

$4 x - 2 y = - 6$

$- 4 x + 2 y = 8$

$4 x - 2 y = - 6$

$- 4 x + 2 y = 8$

Step 1.4

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

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

Step 1.5

Since $0 \neq 2$ , there are no solutions.

No solution

Step 2

Since the system has no solution, the equations and graphs are parallel and do not intersect. Thus, the system is inconsistent.

Inconsistent

Step 3

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

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

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