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anemone
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Find all integer solutions of the system of equations $x+y+z=3$ and $x^3+y^3+z^3=3$.
May be. I would like to know the correct answeranemone said:Sorry kaliprasad, your answer is not quite right...
Integer solutions of a system of equations refer to the values of the variables in the equations that result in whole number solutions. These solutions can be represented as ordered pairs or triplets, depending on the number of variables in the system.
To find integer solutions, you can use various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to isolate the variables and then plugging in different integer values to see which ones satisfy all of the equations in the system.
Yes, a system of equations can have multiple integer solutions. This occurs when there are more equations than variables, resulting in an infinite number of solutions. It can also happen when there are equal or parallel lines in the system, resulting in an infinite number of solutions.
If a system of equations has no integer solutions, it means that there are no values of the variables that satisfy all of the equations in the system. This could happen if the equations are inconsistent or if they represent parallel lines that never intersect.
Yes, a system of equations with integer solutions can also have non-integer solutions. This can occur when the equations involve fractions or decimals, resulting in solutions that are not whole numbers. It is important to specify whether the solutions should be integers or not when solving a system of equations.