Question

For the system shown below, what are the coordinates of the solution that lies in quadrant I?

Write your answer in the form (a,b) without using spaces.

3y^2-5x^2=7
3y^2-x^2=23

Answer 1

3y^2 - 5x^2 = 7
3y^2 = 7 + 5x^2
y = √[(7 + 5x^2)/3]

3y^2 - x^2 = 23
3√[(7 + 5x^2)/3]^2 - x^2 = 23
(7 + 5x^2) - x^2 = 23
4x^2 = 16
x^2 = 4
x = -2 [Not +2 because in the second quadrant, x is negative]

y = √[(7 + 5x^2)/3]
y = √[(7 + 5(-2)^2)/3]
y = √[(7 + 20)/3]
y = √9
y = +3 [Not -3 because in the 2nd quadrant y is positive]

(-2,3)

Answer 2

ah its (2,3) it said :/ but thanks !