Which system of equations has an infinite number of solutions? A. 2x – 6y = 18 x – y = 9 B. 2x – 6

Question

Which system of equations has an infinite number of solutions?

A. 2x – 6y = 18
x – y = 9

B. 2x – 6y = 18
x + 3y = 9

C. 2x – 6y = 18
x – 3y = 9

in progress 0
Emery 4 days 2021-10-10T01:55:27+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T01:56:45+00:00

    Answer:

    your last option

    Step-by-step explanation

    i got it right on edge

    0
    2021-10-10T01:56:45+00:00

    Answer:

    we choose C

    Step-by-step explanation:

    We need to understand an infinite number of solutions happens when all numbers are solutions. This situation means that there is no one solution.

    So let analyse 3 options:

    A.

    • 2x – 6y = 18  (1)
    • x – y = 9  <=> y = x -9 (2)

    Substitute (2) in (1) we have:

    2x – 6(x – 9)  = 18

    <=> -4x + 54 = 18

    <=> x = 9

    => y = 0

    There is only 1 solution => A is wrong

    B.

    • 2x – 6y = 18  <=> x = 9 + 3y (1)
    • x + 3y = 9 (2)

    Substitute (1) in (2) we have:

    (9+ 3y) + 3y = 9

    <=> 3y = 0

    <=> y = 0

    => x = 9

    There is only 1 solution => B is wrong

    C.

    2x – 6y = 18  (1)

    x – 3y = 9 <=> x = 9+ 3y (2)

    Substitute (2) in (1) we have:  

    2(9+3y) – 6y = 18

    <=> 18 + 6y – 6y = 18

    <=> 18=18

    Yes, this system of equations has an infinite number of solutions

    So we choose C

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