Precalculus Examples

3 x - 4 y = 4

$3 x - 4 y = 4$ ,

x + 3 y = - 3

$x + 3 y = - 3$

Step 1

Multiply each equation by the value that makes the coefficients of

x

$x$ opposite.

3 x - 4 y = 4

$3 x - 4 y = 4$

(- 3) \cdot (x + 3 y) = (- 3) (- 3)

$(- 3) \cdot (x + 3 y) = (- 3) (- 3)$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify

(- 3) \cdot (x + 3 y)

$(- 3) \cdot (x + 3 y)$ .

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 3 (3 y) = (- 3) (- 3)

$- 3 x - 3 (3 y) = (- 3) (- 3)$

Step 2.1.1.2

Multiply

3

$3$ by

- 3

$- 3$ .

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = (- 3) (- 3)

$- 3 x - 9 y = (- 3) (- 3)$

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = (- 3) (- 3)

$- 3 x - 9 y = (- 3) (- 3)$

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = (- 3) (- 3)

$- 3 x - 9 y = (- 3) (- 3)$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Multiply

- 3

$- 3$ by

- 3

$- 3$ .

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = 9

$- 3 x - 9 y = 9$

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = 9

$- 3 x - 9 y = 9$

3 x - 4 y = 4

$3 x - 4 y = 4$

- 3 x - 9 y = 9

$- 3 x - 9 y = 9$

Step 3

Add the two equations together to eliminate

x

$x$ from the system.

		$3$ $3$	$x$ $x$		$-$ $-$	$4$ $4$	$y$ $y$	$=$ $=$	$4$ $4$
$+$ $+$	$-$ $-$	$3$ $3$	$x$ $x$		$-$ $-$	$9$ $9$	$y$ $y$	$=$ $=$	$9$ $9$
				$-$ $-$	$1$ $1$	$3$ $3$	$y$ $y$	$=$ $=$	$1$ $1$	$3$ $3$

Step 4

Divide each term in

- 13 y = 13

$- 13 y = 13$ by

- 13

$- 13$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in

- 13 y = 13

$- 13 y = 13$ by

- 13

$- 13$ .

\frac{- 13 y}{- 13} = \frac{13}{- 13}

$\frac{- 13 y}{- 13} = \frac{13}{- 13}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of

- 13

$- 13$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

\frac{- 13 y}{- 13} = \frac{13}{- 13}

$\frac{- 13 y}{- 13} = \frac{13}{- 13}$

Step 4.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{13}{- 13}

$y = \frac{13}{- 13}$

y = \frac{13}{- 13}

$y = \frac{13}{- 13}$

y = \frac{13}{- 13}

$y = \frac{13}{- 13}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide

13

$13$ by

- 13

$- 13$ .

y = - 1

$y = - 1$

y = - 1

$y = - 1$

y = - 1

$y = - 1$

Step 5

Substitute the value found for

y

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

x

$x$ .

Tap for more steps...

Step 5.1

Substitute the value found for

y

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

x

$x$ .

3 x - 4 \cdot - 1 = 4

$3 x - 4 \cdot - 1 = 4$

Step 5.2

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

3 x + 4 = 4

$3 x + 4 = 4$

Step 5.3

Move all terms not containing

x

$x$ to the right side of the equation.

Tap for more steps...

Step 5.3.1

Subtract

4

$4$ from both sides of the equation.

3 x = 4 - 4

$3 x = 4 - 4$

Step 5.3.2

Subtract

4

$4$ from

4

$4$ .

3 x = 0

$3 x = 0$

3 x = 0

$3 x = 0$

Step 5.4

Divide each term in

3 x = 0

$3 x = 0$ by

3

$3$ and simplify.

Tap for more steps...

Step 5.4.1

Divide each term in

3 x = 0

$3 x = 0$ by

3

$3$ .

\frac{3 x}{3} = \frac{0}{3}

$\frac{3 x}{3} = \frac{0}{3}$

Step 5.4.2

Simplify the left side.

Tap for more steps...

Step 5.4.2.1

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 5.4.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{0}{3}

$\frac{3 x}{3} = \frac{0}{3}$

Step 5.4.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{0}{3}

$x = \frac{0}{3}$

x = \frac{0}{3}

$x = \frac{0}{3}$

x = \frac{0}{3}

$x = \frac{0}{3}$

Step 5.4.3

Simplify the right side.

Tap for more steps...

Step 5.4.3.1

Divide

0

$0$ by

3

$3$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 6

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

(0, - 1)

$(0, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

(0, - 1)

$(0, - 1)$

Equation Form:

x = 0, y = - 1

$x = 0, y = - 1$

Step 8