Answer
$(2, 4)$
$(-5/2, 7/4)$
Work Step by Step
Given the system of equations:
1. $x^2 + y = 8$
2. $x - 2y = -6$
It asks to find all solutions.
Double equation one, and add the result to equation two
$2x^2 + 2y = 16$
+ ($x - 2y = -6)$
$2x^2 + x = 10$
$2x^2 + x - 10 = 0$
$(2x +5)(x - 2) = 0$
$x = 2, -5/2$
Substitute the values into the equation
$2^2 + y = 8$
$y = 4$
$(-5/2)^2 + y = 8$
$y = 7/4$
All solutions:
$(2, 4)$
$(-5/2, 7/4)$
