Final answer:
To solve the given system of equations, substitute y from the first linear equation into the second quadratic equation, solve for x, and then find the corresponding y values.
Step-by-step explanation:
To solve the given system of equations, we use substitution or elimination methods. The system given is:
- y = (3/4)x + 1
- y = (x - 2)² + 1
First, let's identify the first equation as Equation A and the second one as Equation B, then we substitute the y from Equation A into Equation B:
- (3/4)x + 1 = (x - 2)² + 1
- Simplify and expand the square on the right side.
- Move all terms to one side to get a quadratic equation.
- Factor or use the quadratic formula to find the solutions for x.
- Substitute the solutions for x back into either Equation A or B to find the corresponding y values.
By solving the quadratic, we will find the solutions for the intersection points of the two equations, which is the solution to our system.