Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the solution of the linear-quadratic system of equations?
{y=x2−2x+1y−2x=1
To solve the linear-quadratic system of equations {y=x^2−2x+1, y−2x=1}, we can use substitution method.
Step 1: Solve the linear equation for y in terms of x.
y - 2x = 1
y = 2x + 1
Step 2: Substitute the expression for y in terms of x into the quadratic equation.
x^2 - 2x + 1 = 2x + 1
Step 3: Simplify and solve for x.
x^2 - 2x - 2x = 0
x^2 - 4x = 0
x(x - 4) = 0
Using the zero-product property, we set each factor equal to zero:
x = 0
x - 4 = 0
x = 4
Step 4: Substitute the x-values back into the linear equation to find the corresponding y-values.
For x = 0:
y = 2(0) + 1
y = 1
For x = 4:
y = 2(4) + 1
y = 9
Therefore, the solution to the linear-quadratic system of equations is (0, 1) and (4, 9).