Algebra Examples

$3 x + 8 y - 7 = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $3 x$ from both sides of the equation.

$8 y - 7 = - 3 x$

Step 1.1.2

Add $7$ to both sides of the equation.

$8 y = - 3 x + 7$

Step 1.2

Divide each term in $8 y = - 3 x + 7$ by $8$ and simplify.

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Step 1.2.1

Divide each term in $8 y = - 3 x + 7$ by $8$ .

$\frac{8 y}{8} = \frac{- 3 x}{8} + \frac{7}{8}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 3 x}{8} + \frac{7}{8}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 x}{8} + \frac{7}{8}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$y = - \frac{3 x}{8} + \frac{7}{8}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - \frac{3 (0)}{8} + \frac{7}{8}$

Step 3.2

Simplify $- \frac{3 (0)}{8} + \frac{7}{8}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 0 + 7}{8}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $- 3$ by $0$ .

$y = \frac{0 + 7}{8}$

Step 3.2.2.2

Add $0$ and $7$ .

$y = \frac{7}{8}$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, \frac{7}{8})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{3 (1)}{8} + \frac{7}{8}$

Step 4.2

Simplify $- \frac{3 (1)}{8} + \frac{7}{8}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 1 + 7}{8}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $- 3$ by $1$ .

$y = \frac{- 3 + 7}{8}$

Step 4.2.2.2

Add $- 3$ and $7$ .

$y = \frac{4}{8}$

Step 4.2.3

Cancel the common factor of $4$ and $8$ .

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Step 4.2.3.1

Factor $4$ out of $4$ .

$y = \frac{4 (1)}{8}$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $4$ out of $8$ .

$y = \frac{4 \cdot 1}{4 \cdot 2}$

Step 4.2.3.2.2

Cancel the common factor.

$y = \frac{4 \cdot 1}{4 \cdot 2}$

Step 4.2.3.2.3

Rewrite the expression.

$y = \frac{1}{2}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{1}{2})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - \frac{3 (2)}{8} + \frac{7}{8}$

Step 5.2

Simplify $- \frac{3 (2)}{8} + \frac{7}{8}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 2 + 7}{8}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $- 3$ by $2$ .

$y = \frac{- 6 + 7}{8}$

Step 5.2.2.2

Add $- 6$ and $7$ .

$y = \frac{1}{8}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{1}{8})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{7}{8}), (1, \frac{1}{2}), (2, \frac{1}{8})$

Step 7