Algebra Examples

$\frac{2}{3} x + y - 1 = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} + y - 1 = 0$

Step 1.2

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

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Step 1.2.1

Subtract $\frac{2 x}{3}$ from both sides of the equation.

$y - 1 = - \frac{2 x}{3}$

Step 1.2.2

Add $1$ to both sides of the equation.

$y = - \frac{2 x}{3} + 1$

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.

$y = - \frac{2 (0)}{3} + 1$

Step 3.2

Simplify $- \frac{2 (0)}{3} + 1$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Cancel the common factor of $0$ and $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $2 (0)$ .

$y = - \frac{3 (2 \cdot (0))}{3} + 1$

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $3$ out of $3$ .

$y = - \frac{3 (2 \cdot (0))}{3 (1)} + 1$

Step 3.2.1.1.2.2

Cancel the common factor.

$y = - \frac{3 (2 \cdot (0))}{3 \cdot 1} + 1$

Step 3.2.1.1.2.3

Rewrite the expression.

$y = - \frac{2 \cdot (0)}{1} + 1$

Step 3.2.1.1.2.4

Divide $2 \cdot (0)$ by $1$ .

$y = - (2 \cdot (0)) + 1$

Step 3.2.1.2

Multiply $- (2 \cdot (0))$ .

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Step 3.2.1.2.1

Multiply $2$ by $0$ .

$y = - 0 + 1$

Step 3.2.1.2.2

Multiply $- 1$ by $0$ .

$y = 0 + 1$

Step 3.2.2

Add $0$ and $1$ .

$y = 1$

Step 3.3

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

$(0, 1)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Multiply $2$ by $1$ .

$y = - \frac{2}{3} + 1$

Step 4.2.2

Write $1$ as a fraction with a common denominator.

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

Step 4.2.3

Combine the numerators over the common denominator.

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

Step 4.2.4

Add $- 2$ and $3$ .

$y = \frac{1}{3}$

Step 4.3

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

$(1, \frac{1}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Multiply $2$ by $2$ .

$y = - \frac{4}{3} + 1$

Step 5.2.2

Write $1$ as a fraction with a common denominator.

$y = - \frac{4}{3} + \frac{3}{3}$

Step 5.2.3

Combine the numerators over the common denominator.

$y = \frac{- 4 + 3}{3}$

Step 5.2.4

Add $- 4$ and $3$ .

$y = \frac{- 1}{3}$

Step 5.2.5

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

Step 5.3

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

$(2, - \frac{1}{3})$

Step 6

These are three possible solutions to the equation.

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

Step 7