Pre-Algebra Examples

$2 x - y = 1$

Step 1

Solve the equation for

$y$ .

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Step 1.1

Subtract

$2 x$ from both sides of the equation.

$- y = 1 - 2 x$

Step 1.2

Divide each term in

$- y = 1 - 2 x$ by

$- 1$ and simplify.

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Step 1.2.1

Divide each term in

$- y = 1 - 2 x$ by

$- 1$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2

Divide

$y$ by

$1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide

$1$ by

$- 1$ .

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

Step 1.2.3.1.2

Move the negative one from the denominator of

$\frac{- 2 x}{- 1}$ .

$y = - 1 - 1 \cdot (- 2 x)$

Step 1.2.3.1.3

Rewrite

$- 1 \cdot (- 2 x)$ as

$- (- 2 x)$ .

$y = - 1 - (- 2 x)$

Step 1.2.3.1.4

Multiply

$- 2$ by

$- 1$ .

$y = - 1 + 2 x$

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.

$y = - 1 + 2 (0)$

Step 3.2

Simplify

$- 1 + 2 (0)$ .

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Step 3.2.1

Multiply

$2$ by

$0$ .

$y = - 1 + 0$

Step 3.2.2

Add

$- 1$ and

$0$ .

$y = - 1$

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.

$y = - 1 + 2 (1)$

Step 4.2

Simplify

$- 1 + 2 (1)$ .

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Step 4.2.1

Multiply

$2$ by

$1$ .

$y = - 1 + 2$

Step 4.2.2

Add

$- 1$ and

$2$ .

$y = 1$

Step 4.3

Use the

$x$ and

$y$ values to form the ordered pair.

$(1, 1)$

Step 5

Choose

$2$ to substitute in for

$x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - 1 + 2 (2)$

Step 5.2

Simplify

$- 1 + 2 (2)$ .

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Step 5.2.1

Multiply

$2$ by

$2$ .

$y = - 1 + 4$

Step 5.2.2

Add

$- 1$ and

$4$ .

$y = 3$

Step 5.3

Use the

$x$ and

$y$ values to form the ordered pair.

$(2, 3)$

Step 6

These are three possible solutions to the equation.

$(0, - 1), (1, 1), (2, 3)$

Step 7