what is the solution of the linear-quadratic system of equations

Question

y=x2-2x+1
y-2x=1

Answer 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).