Algebra Examples

$y + 4 x = 3$ $y = - 4 x - 1$

Step 1

Simplify the left side.

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Step 1.1

Reorder $y$ and $4 x$ .

$4 x + y = 3$

$y = - 4 x - 1$

$4 x + y = 3$

$y = - 4 x - 1$

Step 2

Add $4 x$ to both sides of the equation.

$4 x + y = 3, y + 4 x = - 1$

Step 3

Reorder the polynomial.

$4 x + y = - 1$

$4 x + y = 3$

Step 4

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

$4 x + y = 3$

$(- 1) \cdot (4 x + y) = (- 1) (- 1)$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $(- 1) \cdot (4 x + y)$ .

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Step 5.1.1.1

Apply the distributive property.

$4 x + y = 3$

$- 1 (4 x) - 1 y = (- 1) (- 1)$

Step 5.1.1.2

Simplify the expression.

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Step 5.1.1.2.1

Multiply $4$ by $- 1$ .

$4 x + y = 3$

$- 4 x - 1 y = (- 1) (- 1)$

Step 5.1.1.2.2

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

$4 x + y = 3$

$- 4 x - y = (- 1) (- 1)$

$4 x + y = 3$

$- 4 x - y = (- 1) (- 1)$

$4 x + y = 3$

$- 4 x - y = (- 1) (- 1)$

$4 x + y = 3$

$- 4 x - y = (- 1) (- 1)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 1$ by $- 1$ .

$4 x + y = 3$

$- 4 x - y = 1$

$4 x + y = 3$

$- 4 x - y = 1$

$4 x + y = 3$

$- 4 x - y = 1$

Step 6

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

		$4$	$x$	$+$	$y$	$=$	$3$
$+$	$-$	$4$	$x$	$-$	$y$	$=$	$1$
					$0$	$=$	$4$

Step 7

Since $0 \neq 4$ , there are no solutions.

No solution

Step 8