Algebra Examples

$- \frac{5}{7} - \frac{11}{7} x = - y$ $2 y = 7 + 5 x$

Step 1

Multiply each term in $- \frac{5}{7} - \frac{11}{7} x = - y$ by $7$ to eliminate the fractions.

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Step 1.1

Multiply each term in $- \frac{5}{7} - \frac{11}{7} x = - y$ by $7$ .

$- \frac{5}{7} \cdot 7 - \frac{11}{7} x \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Cancel the common factor of $7$ .

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Step 1.2.1.1.1

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$\frac{- 5}{7} \cdot 7 - \frac{11}{7} x \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.1.2

Cancel the common factor.

$\frac{- 5}{7} \cdot 7 - \frac{11}{7} x \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.1.3

Rewrite the expression.

$- 5 - \frac{11}{7} x \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

$- 5 - \frac{11}{7} x \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.2

Combine $x$ and $\frac{11}{7}$ .

$- 5 - \frac{x \cdot 11}{7} \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.3

Cancel the common factor of $7$ .

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Step 1.2.1.3.1

Move the leading negative in $- \frac{x \cdot 11}{7}$ into the numerator.

$- 5 + \frac{- x \cdot 11}{7} \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.3.2

Cancel the common factor.

$- 5 + \frac{- x \cdot 11}{7} \cdot 7 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.3.3

Rewrite the expression.

$- 5 - x \cdot 11 = - y \cdot 7$

$2 y = 7 + 5 x$

$- 5 - x \cdot 11 = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.2.1.4

Multiply $11$ by $- 1$ .

$- 5 - 11 x = - y \cdot 7$

$2 y = 7 + 5 x$

$- 5 - 11 x = - y \cdot 7$

$2 y = 7 + 5 x$

$- 5 - 11 x = - y \cdot 7$

$2 y = 7 + 5 x$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $7$ by $- 1$ .

$- 5 - 11 x = - 7 y$

$2 y = 7 + 5 x$

$- 5 - 11 x = - 7 y$

$2 y = 7 + 5 x$

$- 5 - 11 x = - 7 y$

$2 y = 7 + 5 x$

Step 2

Simplify the left side.

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Step 2.1

Reorder $- 5$ and $- 11 x$ .

$- 11 x - 5 = - 7 y$

$2 y = 7 + 5 x$

$- 11 x - 5 = - 7 y$

$2 y = 7 + 5 x$

Step 3

Simplify the right side.

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Step 3.1

Reorder $7$ and $5 x$ .

$2 y = 5 x + 7$

$- 11 x - 5 = - 7 y$

$2 y = 5 x + 7$

$- 11 x - 5 = - 7 y$

Step 4

Move all terms containing variables to the left.

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Step 4.1

Add $5$ to both sides of the equation.

$- 11 x = - 7 y + 5, 2 y = 5 x + 7$

Step 4.2

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

$- 11 x + 7 y = 5, 2 y = 5 x + 7$

Step 4.3

Subtract $5 x$ from both sides of the equation.

$- 11 x + 7 y = 5, 2 y - 5 x = 7$

Step 5

Reorder the polynomial.

$- 5 x + 2 y = 7$

$- 11 x + 7 y = 5$

Step 6

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

$(- 2) \cdot (- 11 x + 7 y) = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

Step 7

Simplify.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $(- 2) \cdot (- 11 x + 7 y)$ .

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Step 7.1.1.1

Apply the distributive property.

$- 2 (- 11 x) - 2 (7 y) = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

Step 7.1.1.2

Multiply.

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Step 7.1.1.2.1

Multiply $- 11$ by $- 2$ .

$22 x - 2 (7 y) = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

Step 7.1.1.2.2

Multiply $7$ by $- 2$ .

$22 x - 14 y = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

$22 x - 14 y = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

$22 x - 14 y = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

$22 x - 14 y = (- 2) (5)$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $- 2$ by $5$ .

$22 x - 14 y = - 10$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

$22 x - 14 y = - 10$

$(7) \cdot (- 5 x + 2 y) = (7) (7)$

Step 7.3

Simplify the left side.

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Step 7.3.1

Simplify $(7) \cdot (- 5 x + 2 y)$ .

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Step 7.3.1.1

Apply the distributive property.

$22 x - 14 y = - 10$

$7 (- 5 x) + 7 (2 y) = (7) (7)$

Step 7.3.1.2

Multiply.

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Step 7.3.1.2.1

Multiply $- 5$ by $7$ .

$22 x - 14 y = - 10$

$- 35 x + 7 (2 y) = (7) (7)$

Step 7.3.1.2.2

Multiply $2$ by $7$ .

$22 x - 14 y = - 10$

$- 35 x + 14 y = (7) (7)$

$22 x - 14 y = - 10$

$- 35 x + 14 y = (7) (7)$

$22 x - 14 y = - 10$

$- 35 x + 14 y = (7) (7)$

$22 x - 14 y = - 10$

$- 35 x + 14 y = (7) (7)$

Step 7.4

Simplify the right side.

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Step 7.4.1

Multiply $7$ by $7$ .

$22 x - 14 y = - 10$

$- 35 x + 14 y = 49$

$22 x - 14 y = - 10$

$- 35 x + 14 y = 49$

$22 x - 14 y = - 10$

$- 35 x + 14 y = 49$

Step 8

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

		$2$	$2$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$1$	$0$
$+$	$-$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$		$4$	$9$
	$-$	$1$	$3$	$x$					$=$		$3$	$9$

Step 9

Divide each term in $- 13 x = 39$ by $- 13$ and simplify.

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Step 9.1

Divide each term in $- 13 x = 39$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{39}{- 13}$

Step 9.2

Simplify the left side.

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Step 9.2.1

Cancel the common factor of $- 13$ .

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Step 9.2.1.1

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{39}{- 13}$

Step 9.2.1.2

Divide $x$ by $1$ .

$x = \frac{39}{- 13}$

Step 9.3

Simplify the right side.

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Step 9.3.1

Divide $39$ by $- 13$ .

$x = - 3$

Step 10

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

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Step 10.1

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

$22 (- 3) - 14 y = - 10$

Step 10.2

Multiply $22$ by $- 3$ .

$- 66 - 14 y = - 10$

Step 10.3

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

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Step 10.3.1

Add $66$ to both sides of the equation.

$- 14 y = - 10 + 66$

Step 10.3.2

Add $- 10$ and $66$ .

$- 14 y = 56$

Step 10.4

Divide each term in $- 14 y = 56$ by $- 14$ and simplify.

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Step 10.4.1

Divide each term in $- 14 y = 56$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{56}{- 14}$

Step 10.4.2

Simplify the left side.

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Step 10.4.2.1

Cancel the common factor of $- 14$ .

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Step 10.4.2.1.1

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{56}{- 14}$

Step 10.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{56}{- 14}$

Step 10.4.3

Simplify the right side.

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Step 10.4.3.1

Divide $56$ by $- 14$ .

$y = - 4$

Step 11

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

$(- 3, - 4)$

Step 12

The result can be shown in multiple forms.

Point Form:

$(- 3, - 4)$

Equation Form:

$x = - 3, y = - 4$

Step 13

		$2$	$2$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$1$	$0$
$+$	$-$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$		$4$	$9$
	$-$	$1$	$3$	$x$					$=$		$3$	$9$

		$2$	$2$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$1$	$0$
$+$	$-$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$		$4$	$9$
	$-$	$1$	$3$	$x$					$=$		$3$	$9$

		$2$	$2$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$1$	$0$
$+$	$-$	$3$	$5$	$x$	$+$	$1$	$4$	$y$	$=$		$4$	$9$
	$-$	$1$	$3$	$x$					$=$		$3$	$9$