Answer
$(\sqrt 6, 2) (-\sqrt 6, 2)$
Work Step by Step
Given the system of equations:
1. $x^2 + y^2 = 10$
2. $x^2 + 2y^2 - 7y = 0$
It asks to find all solutions.
Subtract equation 1 from equation 2
$x^2 + 2y^2 - 7y = 0$
- ($x^2 + y^2 = 10$)
$y^2 - 7y = -10$
$y^2 - 7y + 10 = 0$
$(y - 2) (y- 5) = 0$
$y = 2, 5$
Substitute the values into the equation
$x^2 + 2^2 = 10$
$x^2 = 6$
$x = +/- \sqrt 6$
$x^2 + 5^2 = 10$
$x^2 = -15$
No solution
Thus the solutions are $(\sqrt 6, 2) (-\sqrt 6, 2)$
