Algebra Examples

$- x + y = 14$ and $- 5 x - 7 y = 10$

Step 1

Add $x$ to both sides of the equation.

$y = 14 + x$

$- 5 x - 7 y = 10$

Step 2

Replace all occurrences of $y$ with $14 + x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 5 x - 7 y = 10$ with $14 + x$ .

$- 5 x - 7 (14 + x) = 10$

$y = 14 + x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 5 x - 7 (14 + x)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- 5 x - 7 \cdot 14 - 7 x = 10$

$y = 14 + x$

Step 2.2.1.1.2

Multiply $- 7$ by $14$ .

$- 5 x - 98 - 7 x = 10$

$y = 14 + x$

$- 5 x - 98 - 7 x = 10$

$y = 14 + x$

Step 2.2.1.2

Subtract $7 x$ from $- 5 x$ .

$- 12 x - 98 = 10$

$y = 14 + x$

$- 12 x - 98 = 10$

$y = 14 + x$

$- 12 x - 98 = 10$

$y = 14 + x$

$- 12 x - 98 = 10$

$y = 14 + x$

Step 3

Solve for $x$ in $- 12 x - 98 = 10$ .

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Step 3.1

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

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Step 3.1.1

Add $98$ to both sides of the equation.

$- 12 x = 10 + 98$

$y = 14 + x$

Step 3.1.2

Add $10$ and $98$ .

$- 12 x = 108$

$y = 14 + x$

$- 12 x = 108$

$y = 14 + x$

Step 3.2

Divide each term in $- 12 x = 108$ by $- 12$ and simplify.

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Step 3.2.1

Divide each term in $- 12 x = 108$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{108}{- 12}$

$y = 14 + x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 12$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{108}{- 12}$

$y = 14 + x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{108}{- 12}$

$y = 14 + x$

$x = \frac{108}{- 12}$

$y = 14 + x$

$x = \frac{108}{- 12}$

$y = 14 + x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $108$ by $- 12$ .

$x = - 9$

$y = 14 + x$

$x = - 9$

$y = 14 + x$

$x = - 9$

$y = 14 + x$

$x = - 9$

$y = 14 + x$

Step 4

Replace all occurrences of $x$ with $- 9$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 14 + x$ with $- 9$ .

$y = 14 - 9$

$x = - 9$

Step 4.2

Simplify $y = 14 - 9$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$y = 14 - 9$

$x = - 9$

$y = 14 - 9$

$x = - 9$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $9$ from $14$ .

$y = 5$

$x = - 9$

$y = 5$

$x = - 9$

$y = 5$

$x = - 9$

$y = 5$

$x = - 9$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 9, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 9, 5)$

Equation Form:

$x = - 9, y = 5$

Step 7