Solve the system of equations If there is no solution enter

Solve the system of equations. (If there is no solution, enter NO SOLUTION.) {y = 2x^2 - x + 4 y = x^2 + 3x + 9 (x, y) = () (smaller x-value) (x, y) = () (larger x-value)

Solution

y = 2x^2 -x +4 ----(1)

y = x^2 +3x +9 ----(2)

Equate equation 1 and 2:

2x^2 -x +4 = x^2 +3x +9

x^2 -4x -5 =0

factorise : x^2 -5x +x -5 =0

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

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

x= -1 ; x=5

So, y = x^2 +3x +9

plug x = -1 ; y = (-1)^2 -3 +9 = 7

x=5 ; y=5^2 -3*5 +9 =19

So, Solution set : smaller set ( -1, 7)

larger set (5 , 19)