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This process is repeated until one variable and one equation remain (namely, the value of the variable).From there, the obtained value is substituted into the equation with 2 variables, allowing a solution to be found for the second variable.
equations with suitable constants so that when the modified equations are added, one of the variables is eliminated.
Once this is done, the system will have effectively been reduced by one variable and one equation.
Then, the system would reduce to a single equation with a single unknown variable just as with the last (fortuitous) example.
If we could only turn the is easily determined: Using this solution technique on a three-variable system is a bit more complex.
In a three-variable system, for example, the solution would be found by the point intersection of three planes in a three-dimensional coordinate space—not an easy scenario to visualize.
Several algebraic techniques exist to solve simultaneous equations.
Usually, though, graphing is not a very efficient way to determine the simultaneous solution set for two or more equations.
It is especially impractical for systems of three or more variables.
In this example, the technique of adding the equations together worked well to produce an equation with a single unknown variable.
What about an example where things aren’t so simple?