Precalculus Examples

$x = 3 t + 6$ , $y = 9 t^{2}$

Step 1

Multiply $3$ by each element of the matrix.

$x = (3 (\frac{\sqrt{y}}{3}), 3 (- \frac{\sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

Step 2

Simplify each element in the matrix.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

$x = (3 (\frac{\sqrt{y}}{3}), 3 (- \frac{\sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

Step 2.1.2

Rewrite the expression.

$x = (\sqrt{y}, 3 (- \frac{\sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

$x = (\sqrt{y}, 3 (- \frac{\sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Move the leading negative in $- \frac{\sqrt{y}}{3}$ into the numerator.

$x = (\sqrt{y}, 3 (\frac{- \sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

Step 2.2.2

Cancel the common factor.

$x = (\sqrt{y}, 3 (\frac{- \sqrt{y}}{3})) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

Step 2.2.3

Rewrite the expression.

$x = (\sqrt{y}, - \sqrt{y}) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

$x = (\sqrt{y}, - \sqrt{y}) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$

$x = (\sqrt{y}, - \sqrt{y}) + 6$

$t = \frac{\sqrt{y}}{3}$

$t = - \frac{\sqrt{y}}{3}$