Question

Which system is equivalent to 3x^2 - 4y^2 = 25
-6x^2 - 2y^2 = 11

Answer choices available:
A) 3x^2 - 4y^2 = 25
12x^2 + 4y^2 = 22

B) 3x^2 - 4y^2 = 25
-12x^2 + 4y^2 = 22

C) 6x^2 - 8y^2 = 25
-6x^2 - 2y^2 = 11

D) 6x^2 - 8y^2 = 50
-6x^2 - 2y^2 = 11

As always, thank you for your help!

Answer 1

For this case we have the following system of equations:

$3x ^ 2 - 4y ^ 2 = 25 -6x ^ 2 - 2y ^ 2 = 11$

We can write a system of equivalent equations.

For this, it is enough to multiply one of the two equations by a scalar.

Multiplying the equation 1 by 2, we have:

$6x ^ 2 - 8y ^ 2 = 50$

Therefore, the new system of equations is:

$6x ^ 2 - 8y ^ 2 = 50 -6x ^ 2 - 2y ^ 2 = 11$

Answer:

A system that is equivalent is:

D) $6x ^ 2 - 8y ^ 2 = 50 -6x ^ 2 - 2y ^ 2 = 11$