An algebra problem by A Former Brilliant Member

Algebra Level 2

If x = 2 t x=2t and y = t 3 − 1 y=\dfrac{t}{3}-1 , then the value of t t for which x = 2 y x=2y is:

− 3 2 -\dfrac{3}{2} 5 2 \dfrac{5}{2} 1 2 \dfrac{1}{2} 3 2 \dfrac{3}{2}

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Hung Woei Neoh
May 9, 2016

x = 2 t y = t 3 − 1 x=2t \quad y=\dfrac{t}{3} - 1

Given that x = 2 y x=2y , substitute it into the first equation:

2 y = 2 t ⟹ y = t 2y=2t \implies y=t

Substitute this into the second equation:

t = t 3 − 1 2 3 t = − 1 t = − 1 × 3 2 = − 3 2 t=\dfrac{t}{3} - 1\\ \dfrac{2}{3}t=-1\\ t=-1 \times \dfrac{3}{2} = \boxed{-\dfrac{3}{2}}

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Did the same way!😀😀

Anurag Pandey - 4 years, 10 months ago

For x = 2 y x=2y , we have 2 t = 2 t 3 − 2 2t=\dfrac{2t}{3}-2 or 4 t 3 = − 2 \dfrac{4t}{3}=-2 or t = − 3 2 t= \dfrac {-3}{2} .

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