Iwkxxusunzidn
Answered

IDNLearn.com provides a user-friendly platform for finding answers to your questions. Discover reliable and timely information on any topic from our network of experienced professionals.

Given an equation, y=mx+b, explain how to create an equation for a second line so that the system will have no solutions or infinitely many solutions.

Sagot :

Sqdancefanidn

Answer:

  no solutions: the y-intercept must be changed

  infinite solutions: the equation must describe the same line

Step-by-step explanation:

No Solutions

For the system of equations to have no solutions, the equations must describe parallel lines. The lines will have the same slope (m), but will have different y-intercepts (b).

The second equation could be ...

  y = mx +b1 . . . . . where b1 ≠ b

__

Infinitely Many Solutions

The two equations of the system must describe the same line. The second equation must reduce to exactly the same equation as the one given: y = mx +b. It could be this equation multiplied by a constant, for example:

  ky = mkx +kb . . . . . equation multiplied by k

Or, it could be rearranged:

  mx -y +b = 0 . . . . . general form

  mx -y = -b . . . . . . . .standard form

  y -b = mx . . . . . . . . point-slope form; line with slope m through point (0, b)

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.