Question

Solve the system of equations below algebraically.

5x^2 + y^2 - x + 20y - 48 = 0
x-2y+3=0

A) (0,0) and (1, 2)
B) (0, 2)
C) (1, -3)
D) (-3,0) and (1, 2)​

Answer 1

D) (-3, 0) and (1, 2).

Explanation:

5x^2 + y^2 - x + 20y - 48 = 0

x - 2y + 3 = 0

From the second equation:

x = 2y - 3 , so we substitute this in the first equation:

5(2y - 3)^2 + y^2 - (2y - 3) + 20y - 48 = 0

5(4y^2 - 12y + 9) + y^2 - 2y + 3 + 20y - 48 = 0

20y^2 - 60y + 45 + y^2 - 2y + 3 + 20y - 48 = 0

21y^2 - 42y = 0

21y(y - 2) = 0

y = 0 , 2.

So when y = 0 x = 2(0) - 3 = -3

and when y = 2 , x = 2(2) - 3 = 1.