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Answer :
This means the two equations represent the same line, and there are infinitely many solutions. The system of equations has infinitely many solutions.
To solve the system of equations using Gaussian elimination, we'll eliminate one variable at a time.
Here's the step-by-step process:
1. Start with the given system of equations:
0.75u + 2.25v = 3 (Equation 1)
6u + 18v = 24 (Equation 2)
2. Multiply Equation 1 by 8 to make the coefficients of u in both equations equal:
6u + 18v = 24 (Equation 1, after multiplication)
6u + 18v = 24 (Equation 2)
3. Subtract Equation 1 from Equation 2:
(6u + 18v) - (6u + 18v) = 24 - 24
0 = 0
4. The resulting equation, 0 = 0, indicates that the system of equations is dependent.
This means the two equations represent the same line, and there are infinitely many solutions.
Therefore, the system of equations has infinitely many solutions.
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