Precalculus Examples

$x = 2 - 3 t$ , $y = 5 + t$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = 2 - 3 t$

Step 2

Rewrite the equation as $2 - 3 t = x$ .

$2 - 3 t = x$

Step 3

Subtract $2$ from both sides of the equation.

$- 3 t = x - 2$

Step 4

Divide each term in $- 3 t = x - 2$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 t = x - 2$ by $- 3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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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 $2$ .

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