How do you find the exact solutions to the system x 2 30 + y 2 6 = 1 and x=y?

y 2 30 + y 2 6 = 1 y 2 30 × 30 + y 2 6 × 30 = 1 × 30 y 2 + 5 y 2 = 30 6 y 2 = 30 y 2 = 30 6 = 5 y 2 − 5 = 0 ( y + 5 ) ( y − 5 ) = 0Hence, either y + 5 = 0 i.e. y = − 5 or y − 5 = 0 i.e. y = 5 Hence, x = y = − 5 or x = y = 5

"How do you find the exact solutions to..." was answered by our experts

Marisol Rivers

Answered question

2022-07-22

How do you find the exact solutions to the system

\frac{x^{2}}{30} + \frac{y^{2}}{6} = 1

and x=y?

Answer & Explanation

Jaylene Tyler

Beginner2022-07-23Added 10 answers

\frac{y^{2}}{30} + \frac{y^{2}}{6} = 1

\frac{y^{2}}{30} \times 30 + \frac{y^{2}}{6} \times 30 = 1 \times 30

y^{2} + 5 y^{2} = 30

6 y^{2} = 30

y^{2} = \frac{30}{6} = 5

y^{2} - 5 = 0

(y + \sqrt{5}) (y - \sqrt{5}) = 0

Hence, either

y + \sqrt{5} = 0

i.e.

y = - \sqrt{5}

y - \sqrt{5} = 0

i.e.

y = \sqrt{5}

Hence,

x = y = - \sqrt{5}

x = y = \sqrt{5}

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