Simultaneous Equations Problem Solving

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.Now, we can apply the substitution technique again to the two equations of 2, 4, and 12, respectively, that satisfy all three equations.

Thus the solution must not lose validity for any of the equations.

Select your options so that your calculations are simple and use any method that suits you.

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.

The terms simultaneous equations and systems of equations refer to conditions where two or more unknown variables are related to each other through an equal number of equations.

For this set of equations, there is but a single combination of values for is equal to a value of 18.

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?

For a given system, we could have one solution, no solutions or infinitely many solutions.

Using the process of substitution​ may not be the quickest nor the easiest approach for a given system of linear equations.