Answer:
we choose C
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