y = 2x ^2 - 3x - 1
y = x-3
First we put the equation in terms of x, we replace y = x-3 in the other equation
y = 2x ^2 - 3x - 1, so we get:
x-3 = 2x^2 - 3x - 1
0 = 2x^2 - 3x - x - 1 + 3
0 = 2x^2 - 4x + 2
We look for a common factor in the equation which is 2:
2 ( x^2 - 2x + 1) = 0
We send the 2 to the other side as a division of 0 so it becomes 0, because 0 divided by anything is 0:
x^2 - 2x + 1 = 0/2
x^2 - 2x + 1 = 0
In ax^2 + bx + c find two numbers that added are b and that multiplied are c, in this case is -1 and -1, because b = -2 and c = 1 and b = (-1) + (-1) b = -2 and c = (-1) • (-1) c = 1, so we get:
(x-1) (x-1) = 0
So we get that:
x - 1 = 0
x = 1
I hope I was helpful.