Can Simultaneous Equations Have Multiple Solutions?

AI Thread Summary
Simultaneous equations can have multiple solutions, but the specific equations presented, 4x + 3x = 28 and 2x + 5x = 42, lead to a single variable scenario. The discussion highlights the importance of correctly interpreting the equations, as the original equations lack a second variable. When reformulated as 4x + 3y = 28 and 2x + 5y = 42, the equations can be solved using the Gaussian method. However, if taken literally, the first equations suggest no solution exists unless the constants are equal. Proper formulation is crucial for determining the nature of solutions in simultaneous equations.
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please help me (Simultaneous Equations)

4x+3x=28
2x+5x=42

how can i sole it from gaussian method :(
 
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How about you first write down the corresponding (augmented) matrix?
 


Or you sure its not:(you just ave one variable)

4x+3y=28
2x+5y=42

or something else?
 


Right, I missed that. I assumed that was what you meant. When taken literally as you posted, there is no solution (unless 28 = 52).
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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