Algebra Examples

$3 a + b = 10$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $b$ from both sides of the equation.

$3 a = 10 - b$

Step 1.2

Divide each term in $3 a = 10 - b$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 a = 10 - b$ by $3$ .

$\frac{3 a}{3} = \frac{10}{3} + \frac{- b}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 a}{3} = \frac{10}{3} + \frac{- b}{3}$

Step 1.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{10}{3} + \frac{- b}{3}$

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.

$a = \frac{10}{3} - \frac{b}{3}$

Step 2

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

Step 3

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

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Step 3.1

Simplify $\frac{10}{3} - \frac{0}{3}$ .

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Step 3.1.1

Combine the numerators over the common denominator.

$a = \frac{10 + 0}{3}$

Step 3.1.2

Add $10$ and $0$ .

$a = \frac{10}{3}$

Step 3.2

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

$(0, \frac{10}{3})$

Step 4

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

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Step 4.1

Simplify $\frac{10}{3} - \frac{1}{3}$ .

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Step 4.1.1

Combine the numerators over the common denominator.

$a = \frac{10 - 1}{3}$

Step 4.1.2

Simplify the expression.

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Step 4.1.2.1

Subtract $1$ from $10$ .

$a = \frac{9}{3}$

Step 4.1.2.2

Divide $9$ by $3$ .

$a = 3$

Step 4.2

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

$(1, 3)$

Step 5

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

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Step 5.1

Simplify $\frac{10}{3} - \frac{2}{3}$ .

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Step 5.1.1

Combine the numerators over the common denominator.

$a = \frac{10 - 2}{3}$

Step 5.1.2

Subtract $2$ from $10$ .

$a = \frac{8}{3}$

Step 5.2

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

$(2, \frac{8}{3})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{10}{3}), (1, 3), (2, \frac{8}{3})$

Step 7