Precalculus Examples

2 x + y = - 2

$2 x + y = - 2$ ,

x + 2 y = 2

$x + 2 y = 2$

Step 1

Multiply each equation by the value that makes the coefficients of

x

$x$ opposite.

2 x + y = - 2

$2 x + y = - 2$

(- 2) \cdot (x + 2 y) = (- 2) (2)

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

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify

(- 2) \cdot (x + 2 y)

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

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

2 x + y = - 2

$2 x + y = - 2$

- 2 x - 2 (2 y) = (- 2) (2)

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

Step 2.1.1.2

Multiply

2

$2$ by

- 2

$- 2$ .

2 x + y = - 2

$2 x + y = - 2$

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

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

2 x + y = - 2

$2 x + y = - 2$

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

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

2 x + y = - 2

$2 x + y = - 2$

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

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

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Multiply

- 2

$- 2$ by

2

$2$ .

2 x + y = - 2

$2 x + y = - 2$

- 2 x - 4 y = - 4

$- 2 x - 4 y = - 4$

2 x + y = - 2

$2 x + y = - 2$

- 2 x - 4 y = - 4

$- 2 x - 4 y = - 4$

2 x + y = - 2

$2 x + y = - 2$

- 2 x - 4 y = - 4

$- 2 x - 4 y = - 4$

Step 3

Add the two equations together to eliminate

x

$x$ from the system.

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

Step 4

Divide each term in

- 3 y = - 6

$- 3 y = - 6$ by

- 3

$- 3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in

- 3 y = - 6

$- 3 y = - 6$ by

- 3

$- 3$ .

\frac{- 3 y}{- 3} = \frac{- 6}{- 3}

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of

- 3

$- 3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Step 4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 6}{- 3}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide

$- 6$ by

$- 3$ .

$y = 2$

Step 5

Substitute the value found for

$y$ into one of the original equations, then solve for

$x$ .

Tap for more steps...

Step 5.1

Substitute the value found for

$y$ into one of the original equations to solve for

$x$ .

$2 x + 2 = - 2$

Step 5.2

Move all terms not containing

$x$ to the right side of the equation.

Tap for more steps...

Step 5.2.1

Subtract

$2$ from both sides of the equation.

$2 x = - 2 - 2$

Step 5.2.2

Subtract

$2$ from

$- 2$ .

$2 x = - 4$

Step 5.3

Divide each term in

$2 x = - 4$ by

$2$ and simplify.

Tap for more steps...

Step 5.3.1

Divide each term in

$2 x = - 4$ by

$2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 5.3.2

Simplify the left side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 5.3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 4}{2}$

Step 5.3.3

Simplify the right side.

Tap for more steps...

Step 5.3.3.1

Divide

$- 4$ by

$2$ .

$x = - 2$

Step 6

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

$(- 2, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 8

Enter YOUR Problem