Question

Solve the system of equations algebraically: x^2 +y^2 =25, y=x^2 +3

Answer 1

`{ \tt{ {x}^(2) + {y}^(2) = 25 - - - \{eqn(a) \}}} \\ { \tt{y = {x}^(2) + 3 - - - \{eqn(b) \} }}`

» substitute y in eqn(a) with y in eqn(b)

`{ \tt{ {x}^(2) + ( {x}^(2) + 3) {}^(2) = 25}} \\ { \tt{ {x}^(2) + ( {x}^(2) + 6x + 9) = 25}} \\ { \tt{2 {x}^(2) + 6x + 9 = 25 }} \\ { \tt{2 {x}^(2) + 6x - 16 = 0}} \\ { \tt{x = 1.7 \: \: and \: \: - 4.7}}`

» Find y in eqn(b)

`{ \tt{y = {x}^(2) + 3 }} \\ { \tt{y = 5.89 \: \: and \: \: 25.09}}`