What is the solution of the linear-quadratic system of equations? {y=x2−2x+1y−2x=1
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To solve the system of equations:
1) Start with the second equation:
y - 2x = 1
2) Rearrange the equation to solve for y:
y = 2x + 1
3) Substitute the value of y in the first equation:
x^2 - 2x + 1 = 2x + 1
4) Simplify the equation:
x^2 - 2x - 2x = 0
5) Combine like terms:
x^2 - 4x = 0
6) Factor out x:
x(x - 4) = 0
7) Set each factor equal to zero:
x = 0, x - 4 = 0
8) Solve for x:
x = 0, x = 4
9) Substitute the values of x back into either of the original equations to solve for y. Let's use the rearranged equation from step 2:
y = 2x + 1
For x = 0, y = 2(0) + 1 = 1
For x = 4, y = 2(4) + 1 = 9
So the solutions to the system of equations are (x, y) = (0, 1) and (x, y) = (4, 9).