Solve the system of equations If there is no solution enter
Solve the system of equations. (If there is no solution, enter NO SOLUTION.) {x^2 - 6x + y^2 = -7 2x + y = 7 (x, y) = () (smaller x-value) (x, y) = () (larger x-value)
Solution
x^2 - 6x + y^2 =-7 ---(1)
2x +y = 7 ----(2)
from 2 : y = 7-2x
So, substitue in equation 1: x^2 -6x +(7-2x)^2 =-7
x^2 -6x +4x^2 -28x +49 = -7
5x^2 -34x + 56 =0
solve using quadratice formula:
we get x= 2.8 , 4
Substutute to get y : y = 7 -2x = 7 -2*2.8 = 1.4
y = 7 -2*4 = -1
Smaller soul. set ( 2.8 ,1.4)
larger solution set ( 4,-1
