Algebra Examples

$5 x - 3 y - 10 = 0$ $x + y - 7 = 0$

Step 1

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

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Step 1.1

Subtract $y$ from both sides of the equation.

$x - 7 = - y$

$5 x - 3 y - 10 = 0$

Step 1.2

Add $7$ to both sides of the equation.

$x = - y + 7$

$5 x - 3 y - 10 = 0$

$x = - y + 7$

$5 x - 3 y - 10 = 0$

Step 2

Replace all occurrences of $x$ with $- y + 7$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x - 3 y - 10 = 0$ with $- y + 7$ .

$5 (- y + 7) - 3 y - 10 = 0$

$x = - y + 7$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (- y + 7) - 3 y - 10$ .

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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.

$5 (- y) + 5 \cdot 7 - 3 y - 10 = 0$

$x = - y + 7$

Step 2.2.1.1.2

Multiply $- 1$ by $5$ .

$- 5 y + 5 \cdot 7 - 3 y - 10 = 0$

$x = - y + 7$

Step 2.2.1.1.3

Multiply $5$ by $7$ .

$- 5 y + 35 - 3 y - 10 = 0$

$x = - y + 7$

$- 5 y + 35 - 3 y - 10 = 0$

$x = - y + 7$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $3 y$ from $- 5 y$ .

$- 8 y + 35 - 10 = 0$

$x = - y + 7$

Step 2.2.1.2.2

Subtract $10$ from $35$ .

$- 8 y + 25 = 0$

$x = - y + 7$

$- 8 y + 25 = 0$

$x = - y + 7$

$- 8 y + 25 = 0$

$x = - y + 7$

$- 8 y + 25 = 0$

$x = - y + 7$

$- 8 y + 25 = 0$

$x = - y + 7$

Step 3

Solve for $y$ in $- 8 y + 25 = 0$ .

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Step 3.1

Subtract $25$ from both sides of the equation.

$- 8 y = - 25$

$x = - y + 7$

Step 3.2

Divide each term in $- 8 y = - 25$ by $- 8$ and simplify.

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Step 3.2.1

Divide each term in $- 8 y = - 25$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 25}{- 8}$

$x = - y + 7$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 25}{- 8}$

$x = - y + 7$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 25}{- 8}$

$x = - y + 7$

$y = \frac{- 25}{- 8}$

$x = - y + 7$

$y = \frac{- 25}{- 8}$

$x = - y + 7$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Dividing two negative values results in a positive value.

$y = \frac{25}{8}$

$x = - y + 7$

$y = \frac{25}{8}$

$x = - y + 7$

$y = \frac{25}{8}$

$x = - y + 7$

$y = \frac{25}{8}$

$x = - y + 7$

Step 4

Replace all occurrences of $y$ with $\frac{25}{8}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - y + 7$ with $\frac{25}{8}$ .

$x = - (\frac{25}{8}) + 7$

$y = \frac{25}{8}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- (\frac{25}{8}) + 7$ .

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Step 4.2.1.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = - \frac{25}{8} + 7 \cdot \frac{8}{8}$

$y = \frac{25}{8}$

Step 4.2.1.2

Combine $7$ and $\frac{8}{8}$ .

$x = - \frac{25}{8} + \frac{7 \cdot 8}{8}$

$y = \frac{25}{8}$

Step 4.2.1.3

Combine the numerators over the common denominator.

$x = \frac{- 25 + 7 \cdot 8}{8}$

$y = \frac{25}{8}$

Step 4.2.1.4

Simplify the numerator.

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Step 4.2.1.4.1

Multiply $7$ by $8$ .

$x = \frac{- 25 + 56}{8}$

$y = \frac{25}{8}$

Step 4.2.1.4.2

Add $- 25$ and $56$ .

$x = \frac{31}{8}$

$y = \frac{25}{8}$

$x = \frac{31}{8}$

$y = \frac{25}{8}$

$x = \frac{31}{8}$

$y = \frac{25}{8}$

$x = \frac{31}{8}$

$y = \frac{25}{8}$

$x = \frac{31}{8}$

$y = \frac{25}{8}$

Step 5

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

$(\frac{31}{8}, \frac{25}{8})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{31}{8}, \frac{25}{8})$

Equation Form:

$x = \frac{31}{8}, y = \frac{25}{8}$

Step 7