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Kennesaw State University

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Problem 11

In Exercises 11 - 20, solve the system by the method of substitution. Check your solution(s) graphically.

$ \left\{\begin{array}{l}2x + y = 6\\-x + y = 0\end{array}\right. $

Answer

$(x, y)=(2,2)$

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## Discussion

## Video Transcript

from gives us a system of equations to X plus y equals six and negative x plus line. It was here that says this all, but using the method of substitution in general that this means we're gonna solve one of these equations for a variable and employees get back into the other. It's just what we do with our 1st 2 steps that determines what method we're using. So I noticed that this one has some good properties that we can use to salt for a variable, mainly because, uh, the wine value has a coefficient of one. You really just want to use either equation because the wind by has a coefficient of one. Just because it makes a little bit easier, I'm choosing the 2nd 1 So if we solve that for why, uh, we're gonna add extra, both sides expos, there's just acts. So we just have that Why is going to be equal to X? So now the substitution part means we're gonna take what we learned from this bottom equation and play that back up top to the first equation with why being eggs, we're gonna have to acts. Plus, and here's a substitution part gonna replace fly with X. Now we have a single variable in a single equation. So weaken you some basic algebra to solve for acts. So two X plus eggs it's just three eggs, three x equaling six. We can divide by three on both sides that we know that access to and then because why is equal to X? We also know that pie is equal to two. What we do with that information, it said these two lines are gonna cross at the 20.22 because those were access to and wise too at the same time, Thank you very much.

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