Algebra Examples

$- 24 - 8 x = 12 y$ $1 + \frac{5}{9} y = - \frac{7}{18} x$

Step 1

Multiply each term in $1 + \frac{5}{9} y = - \frac{7}{18} x$ by $18$ to eliminate the fractions.

Tap for more steps...

Step 1.1

Multiply each term in $1 + \frac{5}{9} y = - \frac{7}{18} x$ by $18$ .

$1 \cdot 18 + \frac{5}{9} y \cdot 18 = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $18$ by $1$ .

$18 + \frac{5}{9} y \cdot 18 = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2.1.2

Combine $\frac{5}{9}$ and $y$ .

$18 + \frac{5 y}{9} \cdot 18 = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2.1.3

Cancel the common factor of $9$ .

Tap for more steps...

Step 1.2.1.3.1

Factor $9$ out of $18$ .

$18 + \frac{5 y}{9} \cdot (9 (2)) = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2.1.3.2

Cancel the common factor.

$18 + \frac{5 y}{9} \cdot (9 \cdot 2) = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2.1.3.3

Rewrite the expression.

$18 + 5 y \cdot 2 = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

$18 + 5 y \cdot 2 = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.2.1.4

Multiply $2$ by $5$ .

$18 + 10 y = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

$18 + 10 y = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

$18 + 10 y = - \frac{7}{18} x \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Combine $x$ and $\frac{7}{18}$ .

$18 + 10 y = - \frac{x \cdot 7}{18} \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.3.2

Cancel the common factor of $18$ .

Tap for more steps...

Step 1.3.2.1

Move the leading negative in $- \frac{x \cdot 7}{18}$ into the numerator.

$18 + 10 y = \frac{- x \cdot 7}{18} \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.3.2.2

Cancel the common factor.

$18 + 10 y = \frac{- x \cdot 7}{18} \cdot 18$

$- 24 - 8 x = 12 y$

Step 1.3.2.3

Rewrite the expression.

$18 + 10 y = - x \cdot 7$

$- 24 - 8 x = 12 y$

$18 + 10 y = - x \cdot 7$

$- 24 - 8 x = 12 y$

Step 1.3.3

Multiply $7$ by $- 1$ .

$18 + 10 y = - 7 x$

$- 24 - 8 x = 12 y$

$18 + 10 y = - 7 x$

$- 24 - 8 x = 12 y$

$18 + 10 y = - 7 x$

$- 24 - 8 x = 12 y$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Reorder $- 24$ and $- 8 x$ .

$- 8 x - 24 = 12 y$

$18 + 10 y = - 7 x$

$- 8 x - 24 = 12 y$

$18 + 10 y = - 7 x$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Reorder $18$ and $10 y$ .

$10 y + 18 = - 7 x$

$- 8 x - 24 = 12 y$

$10 y + 18 = - 7 x$

$- 8 x - 24 = 12 y$

Step 4

Move all terms containing variables to the left.

Tap for more steps...

Step 4.1

Add $24$ to both sides of the equation.

$- 8 x = 12 y + 24, 10 y + 18 = - 7 x$

Step 4.2

Subtract $12 y$ from both sides of the equation.

$- 8 x - 12 y = 24, 10 y + 18 = - 7 x$

Step 4.3

Subtract $18$ from both sides of the equation.

$- 8 x - 12 y = 24, 10 y = - 7 x - 18$

Step 4.4

Add $7 x$ to both sides of the equation.

$- 8 x - 12 y = 24, 10 y + 7 x = - 18$

Step 5

Reorder the polynomial.

$7 x + 10 y = - 18$

$- 8 x - 12 y = 24$

Step 6

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

$(7) \cdot (- 8 x - 12 y) = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the left side.

Tap for more steps...

Step 7.1.1

Simplify $(7) \cdot (- 8 x - 12 y)$ .

Tap for more steps...

Step 7.1.1.1

Apply the distributive property.

$7 (- 8 x) + 7 (- 12 y) = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

Step 7.1.1.2

Multiply.

Tap for more steps...

Step 7.1.1.2.1

Multiply $- 8$ by $7$ .

$- 56 x + 7 (- 12 y) = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

Step 7.1.1.2.2

Multiply $- 12$ by $7$ .

$- 56 x - 84 y = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

$- 56 x - 84 y = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

$- 56 x - 84 y = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

$- 56 x - 84 y = (7) (24)$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Multiply $7$ by $24$ .

$- 56 x - 84 y = 168$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

$- 56 x - 84 y = 168$

$(8) \cdot (7 x + 10 y) = (8) (- 18)$

Step 7.3

Simplify the left side.

Tap for more steps...

Step 7.3.1

Simplify $(8) \cdot (7 x + 10 y)$ .

Tap for more steps...

Step 7.3.1.1

Apply the distributive property.

$- 56 x - 84 y = 168$

$8 (7 x) + 8 (10 y) = (8) (- 18)$

Step 7.3.1.2

Multiply.

Tap for more steps...

Step 7.3.1.2.1

Multiply $7$ by $8$ .

$- 56 x - 84 y = 168$

$56 x + 8 (10 y) = (8) (- 18)$

Step 7.3.1.2.2

Multiply $10$ by $8$ .

$- 56 x - 84 y = 168$

$56 x + 80 y = (8) (- 18)$

$- 56 x - 84 y = 168$

$56 x + 80 y = (8) (- 18)$

$- 56 x - 84 y = 168$

$56 x + 80 y = (8) (- 18)$

$- 56 x - 84 y = 168$

$56 x + 80 y = (8) (- 18)$

Step 7.4

Simplify the right side.

Tap for more steps...

Step 7.4.1

Multiply $8$ by $- 18$ .

$- 56 x - 84 y = 168$

$56 x + 80 y = - 144$

$- 56 x - 84 y = 168$

$56 x + 80 y = - 144$

$- 56 x - 84 y = 168$

$56 x + 80 y = - 144$

Step 8

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

	$-$	$5$	$6$	$x$	$-$	$8$	$4$	$y$	$=$		$1$	$6$	$8$
$+$		$5$	$6$	$x$	$+$	$8$	$0$	$y$	$=$	$-$	$1$	$4$	$4$
						$-$	$4$	$y$	$=$			$2$	$4$

Step 9

Divide each term in $- 4 y = 24$ by $- 4$ and simplify.

Tap for more steps...

Step 9.1

Divide each term in $- 4 y = 24$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{24}{- 4}$

Step 9.2

Simplify the left side.

Tap for more steps...

Step 9.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 9.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{24}{- 4}$

Step 9.2.1.2

Divide $y$ by $1$ .

$y = \frac{24}{- 4}$

Step 9.3

Simplify the right side.

Tap for more steps...

Step 9.3.1

Divide $24$ by $- 4$ .

$y = - 6$

Step 10

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Tap for more steps...

Step 10.1

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$- 56 x - 84 \cdot - 6 = 168$

Step 10.2

Multiply $- 84$ by $- 6$ .

$- 56 x + 504 = 168$

Step 10.3

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 10.3.1

Subtract $504$ from both sides of the equation.

$- 56 x = 168 - 504$

Step 10.3.2

Subtract $504$ from $168$ .

$- 56 x = - 336$

Step 10.4

Divide each term in $- 56 x = - 336$ by $- 56$ and simplify.

Tap for more steps...

Step 10.4.1

Divide each term in $- 56 x = - 336$ by $- 56$ .

$\frac{- 56 x}{- 56} = \frac{- 336}{- 56}$

Step 10.4.2

Simplify the left side.

Tap for more steps...

Step 10.4.2.1

Cancel the common factor of $- 56$ .

Tap for more steps...

Step 10.4.2.1.1

Cancel the common factor.

$\frac{- 56 x}{- 56} = \frac{- 336}{- 56}$

Step 10.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 336}{- 56}$

Step 10.4.3

Simplify the right side.

Tap for more steps...

Step 10.4.3.1

Divide $- 336$ by $- 56$ .

$x = 6$

Step 11

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

$(6, - 6)$

Step 12

The result can be shown in multiple forms.

Point Form:

$(6, - 6)$

Equation Form:

$x = 6, y = - 6$

Step 13

	$-$	$5$	$6$	$x$	$-$	$8$	$4$	$y$	$=$		$1$	$6$	$8$
$+$		$5$	$6$	$x$	$+$	$8$	$0$	$y$	$=$	$-$	$1$	$4$	$4$
						$-$	$4$	$y$	$=$			$2$	$4$

	$-$	$5$	$6$	$x$	$-$	$8$	$4$	$y$	$=$		$1$	$6$	$8$
$+$		$5$	$6$	$x$	$+$	$8$	$0$	$y$	$=$	$-$	$1$	$4$	$4$
						$-$	$4$	$y$	$=$			$2$	$4$

	$-$	$5$	$6$	$x$	$-$	$8$	$4$	$y$	$=$		$1$	$6$	$8$
$+$		$5$	$6$	$x$	$+$	$8$	$0$	$y$	$=$	$-$	$1$	$4$	$4$
						$-$	$4$	$y$	$=$			$2$	$4$