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How can you tell that an equation has the same solution as the original equation?
If the two equations are linear transformations of one another they have the same solution.
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
Does the point (7 0) satisfy the equation y x?
Is (7, 9) a solution to the equation y = x?
How can one tell when a math problem has no solution?
Depends on the type of math problem. there's usually an equation to see if there is a solution or not.
