In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9

Question

System of equations: x + 3y = 8 and y = 2x - 9 for solving by substitution.

Accepted Answer

Hey everyone, welcome back in this problem. We are asked to use the substitution method to solve the system. And the system we're given is two, X plus three, Y equals four and y is equal to x minus seven. Okay, so let's go ahead first and just label our equation. So equation one is going to be two, X plus three, Y equals four. And equation two is going to be Y is equal to x minus seven. Okay. Labeling them just makes it easier to follow through with your work as you go. Alright, now with substitution method, what we wanna do is we wanna isolate one of the variables and one of the equations and substitute it into the other. We can choose either equation and we can choose either variable X or Y. Now in this case in equation to we already see that Y has been isolated. Okay, so that's gonna be an easy choice. So let's go ahead and substitute equation to into equation one. Okay, and this is going to find solutions that satisfy both of those equations. Alright, so we have to X plus three and we have Y. Which is now x minus seven. So three times X minus seven equals four. Okay, expanding on the left hand side, two X plus three X minus 21 is equal to four. Okay let's go ahead and move the 21 over to the right hand side. So all of the numbers are on the right hand side, so on the left we're going to have five X. And on the right we're gonna have 25. Okay, dividing by five. We get X. Is equal to five. Alright so we found an X. Value. Remember we're looking for a solution so we need a corresponding Y value. Okay so now that we have an X. Value, we can substitute that into either equation one or two. Okay. To find why in this case let's substitute it into equation two. That's just gonna be easier. We won't need to rearrange. Okay, so let's substitute X equals five into equation two. Okay and the hard work here is done. We've substituted the equation, the part where we're dealing with equations. Now we're just substituting a number, we know how to do that. Um So let's just go ahead and do that. So we have Y. Is equal to five X minus seven. Then we get Y is equal to -2. Alright, so this is our Y value. So that makes our solution set the 0.5 or X value minus to the Y value. That's going to be the answer. Thanks everyone for watching. See you in the next video

In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9

Verified Solution