"Y" in the second equation has a coefficient of one. For instance, this system of equations has a variable that has a coefficient of one. This is because will be simple to get a variable alone and proceed with this method. The substitution method is best used when a coefficient on a variable is equal to one. Ideo: Problem of the Day: System of EquationsĬtivity: Multiplication/Addition (Elimination) Method Ideo: Solving Systems of Equations: The Multiplication/Addition Method We will leave the reader to verify that the solution is x = -2 and y = -3.
In either case, we can now use the addition method to cancel a single letter from each system, in order to be left with a single variable and one equation. Or, we could multiply the top equation by 3 and the bottom equation by 2. To achieve these opposite coefficients we could multiply the top equation by 4 and the bottom equation by 6 as such. This set of equations requires multiplying both equations by values so that the coefficients on either the x-values or the y-values are opposite in value. However, if the coefficients on the x-terms were opposite in value (like the problem from the addition method section above), we could add the system of equations to end up with a single equation with only one variable. Let us say we had to solve this system of equations.Īdding the two equations as they are right now will not cancel any variable, nor leave us with a single variable. View the following example to get a feel for this this strategy. The technique for preparing the equations is sometimes simple and other times more complicated. It is more probable that our equations will need to be manipulated so we may use the addition method. Most of the equations that we are presented with do not have coefficients that are opposite each other for a single variable like we saw for the example presented within the addition method above.
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