Algebra Examples

$- 7 x + 3 y = 2$

Step 1

Solve the equation for $y$ .

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Step 1.1

Add $7 x$ to both sides of the equation.

$3 y = 2 + 7 x$

Step 1.2

Divide each term in $3 y = 2 + 7 x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y = 2 + 7 x$ by $3$ .

$\frac{3 y}{3} = \frac{2}{3} + \frac{7 x}{3}$

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.

$\frac{3 y}{3} = \frac{2}{3} + \frac{7 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{3} + \frac{7 x}{3}$

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.

$y = \frac{2}{3} + \frac{7 (0)}{3}$

Step 3.2

Simplify $\frac{2}{3} + \frac{7 (0)}{3}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{2 + 7 (0)}{3}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $7$ by $0$ .

$y = \frac{2 + 0}{3}$

Step 3.2.2.2

Add $2$ and $0$ .

$y = \frac{2}{3}$

Step 3.3

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

$(0, \frac{2}{3})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{2}{3} + \frac{7 (1)}{3}$

Step 4.2

Simplify $\frac{2}{3} + \frac{7 (1)}{3}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{2 + 7 (1)}{3}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $7$ by $1$ .

$y = \frac{2 + 7}{3}$

Step 4.2.2.2

Add $2$ and $7$ .

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

Step 4.2.2.3

Divide $9$ by $3$ .

$y = 3$

Step 4.3

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

$(1, 3)$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Combine the numerators over the common denominator.

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

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $7$ by $2$ .

$y = \frac{2 + 14}{3}$

Step 5.2.2.2

Add $2$ and $14$ .

$y = \frac{16}{3}$

Step 5.3

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

$(2, \frac{16}{3})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{2}{3}), (1, 3), (2, \frac{16}{3})$

Step 7