Solve the following system.

x2 + y 2 = 25

2x + y = 10

The solution set { (

a0,

a1), (

a2,

a3) }.

The solution set is { (3, 4), (5, 0) }.

Step-by-step explanation:

x^2 + y^2 = 25

2x + y = 10

We use substitution:

From the second equation y = 10 - 2x.

Substituting for y in the first equation:

x^2 + (10 - 2x) ^2 = 25

x^2 + 100 - 40x + 4x^2 - 25 = 0

5x^2 - 40x + 75 = 0

Divide through by 5:

x^2 - 8x + 15 = 0

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

x = 3, 5.

when x = 3, y = 10 - 2 (3) = 4.

when x = 5, y = 10 - 2 (5) = 0.