Question
y² = x² + 9 ... (Equation 1)
x² + y² = 41 ... (Equation 2)
Substitute (x² + 9) for y² in equation 2
x² + y² = 41 ... (Equation 2)
∴ x² + x² + 9 = 41
2x² + 9 = 41
2x² = 41 - 9
2x² = 32
(2x²)/2 = 32/2
x² = 16
x = +4 OR -4
Substitute 16 for x² in equation 1
y² = x² + 9 ... (Equation 1)
∴ y² = 16 + 9
y² = 25
y = +5 OR -5
Note that these values can be mixed in four ways
(4, -5), (4, 5), (-4, 5), (-4, -5)
The correct answer is the first choice