SOLUTION: I know how to solve systems of linear equations using the substitution method, the addition/subtraction method, the graphing method, and the multiplication with addition/subtractio

Question 8005: I know how to solve systems of linear equations using the substitution method, the addition/subtraction method, the graphing method, and the multiplication with addition/subtraction method. But I have recently come across a problem that asks me to solve the system 5x - 4y =2 and -2x + y = 1 by using the linear combination method. I would really appreciate it if someone could show me how to use this method.
Thanks!
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
In the "linear combination" method, the equations in the system (or multiples of the equations) are added together to eliminate all but one of the variables. When the equations have a single variable, the system can be solved.

Multiply the second equation by 4. The goal is to get each of the two equations to have the same number of one of the variables, (it doesn't matter which variable, but choose the one that is most convenient) so that you can eliminate that variable by adding the equations. So, after multiplying the second equation by 4, we have:

Now, when you add these two equations, the y is eliminated and you are left with:

Once you have one of the variables, you can find the other by substituting the known variable into either of the original equations and solving for the other variable.
You appear to be knowledgeable enough to do this yourself.

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