The system of equations that has only one solution is 2x+4y=6 and 3x-4y=9
From the list of options, we have:
2x+4y=6 and 3x-4y=9
This system of equations has only one solution and the proof is as follows:
Add both equations
2x + 3x + 4y - 4y = 6 + 9
Evaluate
5x = 15
Divide by 5
x = 3
Substitute x = 3 in 2x+4y=6
2(3)+4y=6
This gives
y = 0
So, the solution is (3, 00
Hence, the system of equations that has only one solution is 2x+4y=6 and 3x-4y=9
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