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How many solutions does the system of equations have 9x - 12y = 24 and 3X = 4y
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GPT 3.5
To determine the number of solutions this system of equations has, we can first simplify the second equation:
3X = 4y
Dividing both sides of the equation by 4, we get:
3/4 X = y
Now we substitute this value for y in the first equation:
9x - 12(3/4 X) = 24
Expanding and simplifying, we have:
9x - (36/4)x = 24
9x - 9x = 24
This equation simplifies to 0 = 24, which is not a true statement. Therefore, these equations are inconsistent, and the system has no solutions.
3X = 4y
Dividing both sides of the equation by 4, we get:
3/4 X = y
Now we substitute this value for y in the first equation:
9x - 12(3/4 X) = 24
Expanding and simplifying, we have:
9x - (36/4)x = 24
9x - 9x = 24
This equation simplifies to 0 = 24, which is not a true statement. Therefore, these equations are inconsistent, and the system has no solutions.
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