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expeople1 [14]
3 years ago
10

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

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Step-by-step explanation:

<u>Given equation:</u>

  • 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.

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

  • 3 = 1*10 + b ⇒ b = -7

<u>And the equation:</u>

  • y = 10x - 7

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

<u>To have infinitely many solutions, both equations must be same:</u>

  • y = 2x + 1

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

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

  • y = 2x + 5
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