Question

Which point is the solution to the following system of equations?

x2 + y2 = 13
2x - y = 4

(3, 2)
(2, 3)
(-3, -2)
(-2, -3)

Answer 1

Its the point (3, 2).

Explanation:

x^2 + y^2 = 13

2x - y = 4

From the second equation y = 2x - 4 so substituting in first equation:

x^2 + (2x - 4)^2 = 13

x^2 + 4x^2 - 16x + 16 = 13

5x^2 - 16x + 3 = 0

(5x - 1 )(x - 3) = 0

x = 0.2, 3.

Substitute x = 3 in the second equation:

2(3) - y = 4

y = 6 - 4 = 2.