what is the solution of the linear-quadratic system of equations
y=x2-2x+1
y-2x=1
To find the solution of the linear-quadratic system of equations, we need to solve the two equations simultaneously.
First, let's solve the second equation for y:
y - 2x = 1
y = 2x + 1
Now, we can substitute this expression for y into the first equation:
x^2 - 2x + 1 = 2x + 1
Simplifying this equation, we get:
x^2 - 4x = 0
Factorizing the equation, we have:
x(x - 4) = 0
So, the possible values for x are x = 0 and x = 4.
For x = 0, substitute it back into the second equation:
y = 2(0) + 1
y = 1
Therefore, one solution is (x, y) = (0, 1).
For x = 4, substitute it back into the second equation:
y = 2(4) + 1
y = 9
Therefore, another solution is (x, y) = (4, 9).
The solution of the linear-quadratic system of equations is (0, 1) and (4, 9).