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Use any method to solve the following system o y=(3)/(4)x+1 y=(x-2)²+1

User Golu
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1 Answer

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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:

  1. (3/4)x + 1 = (x - 2)² + 1
  2. Simplify and expand the square on the right side.
  3. Move all terms to one side to get a quadratic equation.
  4. Factor or use the quadratic formula to find the solutions for x.
  5. 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.

User Abdullah
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