Question

Solve the following system.
x^2 + y^2 = 25
2x + y = 10
The solution set

Answer 1

x^2 + y^2 = 25 ...... Equation (1)

2x  + y     = 10

          y    = 10 - 2x ........ Equation (2)

Substituting equation (2) in equation (1), we get,

   x^2 + ( 10 - 2x )^2  = 25

   x^2 + 100 - 40x + 4x^2  = 25

   5x^2 - 40x +100 - 25 = 0

   5x^2 - 40x + 75 = 0

   5 ( x^2 - 8x + 15 ) = 0

  x^2 - 8x + 15  = 0

  x^2 - 5x - 3x + 15 = 0

  x ( x - 5 ) -3 ( x - 5 )  = 0

  ( x -5 ) ( x - 3 ) = 0

Therefore, x = 5 and x = 3

 If x = 5 then, y = 10 - 2(5)

                      y = 10 - 10

                      y = 0

 If x = 3 then, y = 10 - 2(3)

                      y = 10 - 6

                      y = 4

Therefore, solution set = { 5 , 0 } and { 3 , 4 }

Answer 2

answer is C

(0, -5) and (-4, 3)