In Exercises 5–18, solve each system by the substitution metho...

Question

In Exercises 5–18, solve each system by the substitution method. $\begin{cases}x = 4y - 2 \x = 6y + 8\end{cases}$

Accepted Answer

Hey everyone welcome back in this problem. We are asked to use the substitution method to solve the system. The system we're given is X equals y minus seven and x is equal to three, Y minus 17. So let's go ahead and rewrite our equations. Okay we're just going to label them. So equation one will be X equals y minus seven and equation two will be X equals three Y minus 17. And labeling them just makes it easier to refer to them later and I'll make it easier to follow along with our solution. Alright so now with substitution method, what we wanna do is we want to substitute one equation into the other. Okay so we want to isolate one of the variables and one of the equations and then substitute into the other. We see in both of our equations that we already have X isolated. Okay so we don't even have any work to do here. We just need to substitute one into the other and we can choose either one. So in this case we're going to choose to substitute equation one into equation two and again you could do it the other way around if you want it. So equation one, X equals y minus seven. So when we're substituting into equation two we have X which is now y minus seven Is equal to three Y -17. And we'll see now that we've done the substitution, we only have an equation of Y in constant terms we've gotten rid of the X terms and so now we can go ahead and sell for y. Okay so let's move the Y. To the right hand side, the 17 to the left hand side. What we're going to have is 10 is equal to two. Y. Okay this will give us y value equal to five. So we get Y equals five. So now we have a Y value. Now what we have to do is just substitute that Y value back into one of the equations. Okay so we've done the hard work here of substituting the whole equation now we're just substituting a value. Okay? Alright so we can choose equation one or equation to let's go ahead and choose equation um One. So let's Y equals five into equation one. Okay we're gonna have X is equal to 5 -7. That's gonna give us X. is equal to -2. Okay And so our solution set is going to contain the point minus 25. Okay. Are X and Y. Value that we found? And that is going to correspond with answer C. Thanks for watching everyone. I hope this video helped see you in the next one.

In Exercises 5–18, solve each system by the substitution method. $\begin{cases}\)x = 4y - 2 \\(\x\) = 6y + 8\(\end{cases}$

Key Concepts

System of Linear Equations

Substitution Method

Solving Linear Equations

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