Solving Problems With Two Variables

Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations. \[\begin3x - y & = 7\ 2x 3y & = 1\end\] Before we discuss how to solve systems we should first talk about just what a solution to a system of equations is.A solution to a system of equations is a value of \(x\) and a value of \(y\) that, when substituted into the equations, satisfies both equations at the same time.

\[\beginax by & = p\ cx dy & = q\end\] where any of the constants can be zero with the exception that each equation must have at least one variable in it.

It is quite possible that a mistake could result in a pair of numbers that would satisfy one of the equations but not the other one.

Let’s now move into the next method for solving systems of equations. If fractions are going to show up they will only show up in the final step and they will only show up if the solution contains fractions.

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