Algebra Examples

y + 4 x = 3

$y + 4 x = 3$

y = - 4 x - 1

$y = - 4 x - 1$

Step 1

Simplify the left side.

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Step 1.1

Reorder

y

$y$ and

4 x

$4 x$ .

4 x + y = 3

$4 x + y = 3$

y = - 4 x - 1

$y = - 4 x - 1$

4 x + y = 3

$4 x + y = 3$

y = - 4 x - 1

$y = - 4 x - 1$

Step 2

Add

4 x

$4 x$ to both sides of the equation.

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

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

Step 3

Reorder the polynomial.

4 x + y = - 1

$4 x + y = - 1$

4 x + y = 3

$4 x + y = 3$

Step 4

Multiply each equation by the value that makes the coefficients of

y

$y$ opposite.

4 x + y = 3

$4 x + y = 3$

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

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

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)

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

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Step 5.1.1.1

Apply the distributive property.

4 x + y = 3

$4 x + y = 3$

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

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

Step 5.1.1.2

Simplify the expression.

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Step 5.1.1.2.1

Multiply

4

$4$ by

- 1

$- 1$ .

4 x + y = 3

$4 x + y = 3$

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

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

Step 5.1.1.2.2

Rewrite

- 1 y

$- 1 y$ as

- y

$- y$ .

4 x + y = 3

$4 x + y = 3$

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

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

4 x + y = 3

$4 x + y = 3$

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

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

4 x + y = 3

$4 x + y = 3$

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

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

4 x + y = 3

$4 x + y = 3$

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

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

4 x + y = 3

$4 x + y = 3$

- 4 x - y = 1

$- 4 x - y = 1$

4 x + y = 3

$4 x + y = 3$

- 4 x - y = 1

$- 4 x - y = 1$

4 x + y = 3

$4 x + y = 3$

- 4 x - y = 1

$- 4 x - y = 1$

Step 6

Add the two equations together to eliminate

y

$y$ from the system.

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

Step 7

Since

0 \neq 4

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

No solution

Step 8

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$