Answer
No Solutions
Work Step by Step
Given the system of equations:
1. $x^2 + 2y^2 = 2$
2. $2x^2 - 3y = 15$
It asks to find all solutions.
Double equation one, subtract equation two out of equation one
$2x^2 + 4y^2 = 4$
-($2x^2 - 3y = 15$)
$4y^2 + 3y = -11$
$4(y^2 + 3/4 y +9/64) = -11 + 9/16$
$(y + 3/8)^2 = -167/64$
No solutions here since the right side will be imaginary.
Thus, no solutions for the system of equations
