Precalculus Examples

x = 2 - 3 t

$x = 2 - 3 t$ ,

y = 5 + t

$y = 5 + t$

Step 1

Set up the parametric equation for

x (t)

$x (t)$ to solve the equation for

t

$t$ .

x = 2 - 3 t

$x = 2 - 3 t$

Step 2

Rewrite the equation as

2 - 3 t = x

$2 - 3 t = x$ .

2 - 3 t = x

$2 - 3 t = x$

Step 3

Subtract

2

$2$ from both sides of the equation.

- 3 t = x - 2

$- 3 t = x - 2$

Step 4

Divide each term in

- 3 t = x - 2

$- 3 t = x - 2$ by

- 3

$- 3$ and simplify.

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Step 4.1

Divide each term in

- 3 t = x - 2

$- 3 t = x - 2$ by

- 3

$- 3$ .

\frac{- 3 t}{- 3} = \frac{x}{- 3} + \frac{- 2}{- 3}

$\frac{- 3 t}{- 3} = \frac{x}{- 3} + \frac{- 2}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 t}{- 3} = \frac{x}{- 3} + \frac{- 2}{- 3}$

Step 4.2.1.2

Divide

$t$ by

$1$ .

$t = \frac{x}{- 3} + \frac{- 2}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$t = - \frac{x}{3} + \frac{- 2}{- 3}$

Step 4.3.1.2

Dividing two negative values results in a positive value.

$t = - \frac{x}{3} + \frac{2}{3}$

Step 5

Replace

$t$ in the equation for

$y$ to get the equation in terms of

$x$ .

$y = 5 - \frac{x}{3} + \frac{2}{3}$

Step 6

Remove parentheses.

$y = 5 - \frac{x}{3} + \frac{2}{3}$

Step 7

Simplify

$5 - \frac{x}{3} + \frac{2}{3}$ .

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Step 7.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$y = - \frac{x}{3} + 5 \cdot \frac{3}{3} + \frac{2}{3}$

Step 7.2

Combine

$5$ and

$\frac{3}{3}$ .

$y = - \frac{x}{3} + \frac{5 \cdot 3}{3} + \frac{2}{3}$

Step 7.3

Combine the numerators over the common denominator.

$y = - \frac{x}{3} + \frac{5 \cdot 3 + 2}{3}$

Step 7.4

Simplify the numerator.

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Step 7.4.1

Multiply

$5$ by

$3$ .

$y = - \frac{x}{3} + \frac{15 + 2}{3}$

Step 7.4.2

Add

$15$ and

$2$ .

$y = - \frac{x}{3} + \frac{17}{3}$