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

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