Question

How many solutions are there for the system shown below?

x^2+4y^2=100
4y-x^2=-20


A. 4
B. 3
C. 1
D. 2

Answer 1

x^2+4y^2=100 -(1)
4y-x^2=-20 => x^2 = 4y+20 - (2)
Put (2) into (1) and solve for y, see how many solution(s) you can get
Then solve x using the value of y, and determine the number of solution(s) of x
Can you do it now?

Answer 2

4y^2 + x^2 + 4y - x^2 = 100 - 20
4y^2 + 4y = 80
y^2 + y = 20
y^2 + y - 20 = 0
y = (-1 +/- sqrt(1 + 80)) / 2
y = (-1 +/- 9) / 2
y = -10/2 , 8/2
y = -5 , 4

4y - x^2 = -20
4 * (-5) - x^2 = -20
-20 - x^2 = -20
0 = x^2
x = 0

4 * 4 - x^2 = -20
16 - x^2 = -20
36 = x^2
x = -6 , 6

Solutions:

(0 , -5)
(-6 , 4)
(6 , 4)