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.

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