Question

One equation in a system of linear equations is y=2x+1

a. write a second equation so that (1,3) is the only solution of the system


b. Write a second equation so that the system has infinitely many solutions


c. Write a second equation so that the system has no solutions


would appreciate answers

Answer 1

Explanation:

Given equation:

• y = 2x + 1

a. write a second equation so that (1,3) is the only solution of the system

To have only one solution the equation must have a different slope.

Let it be 10, then the y-intercept of y = 10x + b is:

• 3 = 1*10 + b ⇒ b = -7

And the equation:

• y = 10x - 7

b. Write a second equation so that the system has infinitely many solutions

To have infinitely many solutions, both equations must be same:

• y = 2x + 1

c. Write a second equation so that the system has no solutions.

To have no solutions, the equations must have same slope but different y-intercepts:

• y = 2x + 5