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

Answer 1

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