We are give that:
y = 3x^2 - 8x -2
Thus, y is given in terms of x. We will use this to substitute in the second equation and get the values of x as follows:
2x - y = 5
2x - (3x^2 - 8x -2) = 5
2x - 3x^2 + 8x + 2 -5 = 0
-3x^2 + 10x - 3 = 0
(x-3) (3x-1) = 0
either x = 3
or x = 1/3
Now, we will use the calculated values of x to find y as follows:
At x=3: y = 3x^2 - 8x - 2 = 3(3)^2 - 8(3) - 2 = 1
At x=1/3 : y = 3x^2 - 8x - 2 = 3(1/3)^2 - 8(1/3) - 2 = -13/3
Based on the above calculations, the solution sets of the system of equations given are either (3,1) or (1/3 , -13/3)
