Precalculus Examples

$10 x - 7 y = 8$ , $2 x - 37 = - 8$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Add $37$ to both sides of the equation.

$10 x - 7 y = 8, 2 x = - 8 + 37$

Step 1.2

Add $- 8$ and $37$ .

$10 x - 7 y = 8, 2 x = 29$

Step 2

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

$10 x - 7 y = 8$

$(- 5) \cdot (2 x) = (- 5) (29)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Multiply $2$ by $- 5$ .

$10 x - 7 y = 8$

$- 10 x = (- 5) (29)$

$10 x - 7 y = 8$

$- 10 x = (- 5) (29)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 5$ by $29$ .

$10 x - 7 y = 8$

$- 10 x = - 145$

$10 x - 7 y = 8$

$- 10 x = - 145$

$10 x - 7 y = 8$

$- 10 x = - 145$

Step 4

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

		$1$	$0$	$x$	$-$	$7$	$y$	$=$				$8$
$+$	$-$	$1$	$0$	$x$				$=$	$-$	$1$	$4$	$5$
					$-$	$7$	$y$	$=$	$-$	$1$	$3$	$7$

Step 5

Divide each term in $- 7 y = - 137$ by $- 7$ and simplify.

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Step 5.1

Divide each term in $- 7 y = - 137$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 137}{- 7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 137}{- 7}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 137}{- 7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$y = \frac{137}{7}$

Step 6

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

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Step 6.1

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

$10 x - 7 (\frac{137}{7}) = 8$

Step 6.2

Simplify each term.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Factor $7$ out of $- 7$ .

$10 x + 7 (- 1) \frac{137}{7} = 8$

Step 6.2.1.2

Cancel the common factor.

$10 x + 7 \cdot - 1 \frac{137}{7} = 8$

Step 6.2.1.3

Rewrite the expression.

$10 x - 1 \cdot 137 = 8$

Step 6.2.2

Multiply $- 1$ by $137$ .

$10 x - 137 = 8$

Step 6.3

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

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Step 6.3.1

Add $137$ to both sides of the equation.

$10 x = 8 + 137$

Step 6.3.2

Add $8$ and $137$ .

$10 x = 145$

Step 6.4

Divide each term in $10 x = 145$ by $10$ and simplify.

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Step 6.4.1

Divide each term in $10 x = 145$ by $10$ .

$\frac{10 x}{10} = \frac{145}{10}$

Step 6.4.2

Simplify the left side.

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Step 6.4.2.1

Cancel the common factor of $10$ .

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Step 6.4.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{145}{10}$

Step 6.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{145}{10}$

Step 6.4.3

Simplify the right side.

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Step 6.4.3.1

Cancel the common factor of $145$ and $10$ .

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Step 6.4.3.1.1

Factor $5$ out of $145$ .

$x = \frac{5 (29)}{10}$

Step 6.4.3.1.2

Cancel the common factors.

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Step 6.4.3.1.2.1

Factor $5$ out of $10$ .

$x = \frac{5 \cdot 29}{5 \cdot 2}$

Step 6.4.3.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot 29}{5 \cdot 2}$

Step 6.4.3.1.2.3

Rewrite the expression.

$x = \frac{29}{2}$

Step 7

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

$(\frac{29}{2}, \frac{137}{7})$

Step 8

The result can be shown in multiple forms.

Point Form:

$(\frac{29}{2}, \frac{137}{7})$

Equation Form:

$x = \frac{29}{2}, y = \frac{137}{7}$

Step 9

		$1$	$0$	$x$	$-$	$7$	$y$	$=$				$8$
$+$	$-$	$1$	$0$	$x$				$=$	$-$	$1$	$4$	$5$
					$-$	$7$	$y$	$=$	$-$	$1$	$3$	$7$

		$1$	$0$	$x$	$-$	$7$	$y$	$=$				$8$
$+$	$-$	$1$	$0$	$x$				$=$	$-$	$1$	$4$	$5$
					$-$	$7$	$y$	$=$	$-$	$1$	$3$	$7$

		$1$	$0$	$x$	$-$	$7$	$y$	$=$				$8$
$+$	$-$	$1$	$0$	$x$				$=$	$-$	$1$	$4$	$5$
					$-$	$7$	$y$	$=$	$-$	$1$	$3$	$7$