Which of the following is a solution to the system shown below? y = 3x 2 - 8x - 2 and 2x - y = 5
Accepted Solution
A:
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)