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Q: How many solutions exist for the following system of equations?

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There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.

No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.

A homogeneous system of eqs: Ax=0 will always be consistent, since x=0 is always a possible solution. However, if det(A)=0 then there will be infinite solutions, as |A|=0 implies that either no solutions or infinitely many exist, and it is impossible for no solutions to exist to Ax=0. If det(A) is non 0, then x=0 is the only solution, as |A| is not equal to 0 implies a unique solution only!(in this case x=0). Hope this helps!

Equations are balanced in chemistry (several exceptions exist).

Solutions that exist in nature include oceans that have water and trace metals. Acid rain and petroleum are other solutions that exist in nature.

No

No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.

No, solid solutions also exist.

Wormholes are not proven to exist. There are mathematical theories that they may, however there are several different solutions to the equations. The most likely is that you would simply disappear, effectively you would die. There are low probability solutions that you may emerge elsewhere or elsewhen but these solutions are by no means clear.

Ferric ions exist in solutions.

x+y=0 2x+2y=0 This homogeneous system has infinitely many non-trivial solutions. If you are looking for exactly one non-trivial solution, no such system exists. the system may or may not have non trivial solution. if number of variables equal to number of equations and given matrix is non singular then non trivial solution does not exist

She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.

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