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Q: A system of linear equation in two variables can have how many solutions?

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Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.

A linear equation in n variables, x1, x2, ..., xn is an equation of the forma1x1 + a2x2 + ... + anxn = y where the ai are constants.A system of linear equations is a set of m linear equations in n unknown variables. There need not be any relationship between m and n. The system may have none, one or many solutions.

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A.infinitely manyB.oneD.zero

Yes.

There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.

The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.

There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.

No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions

4x + 2y = 6

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

None, one or infinitely many.

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