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

Question

In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x

Exercise 5: Solve the system of equations x + y = 4 and y = 3x using substitution.

Accepted Answer

Everyone in this problem, we're asked to use the substitution method to solve the system. And the system we're given is X minus Y equals three and Y is equal to minus two X. OK. So a system of two equations, let's go ahead first and label our equations. So equation one is going to be X minus Y equals three. And equation two is going to be Y equals minus two X. OK. And labeling them just makes it easier to follow through with their work. All right. So with substitution method, the first thing we want to do is isolate one of the variables from one of the equations. OK. So we can choose either equation one or two and we can choose to isolate either X or Y. Now, if we look at equation two, we've already have Y isolated. OK. So that part has already been done for us. So let's choose equation two. We're gonna substitute that into the other equation. Equation one. OK. So that we're finding solutions that satisfy both of those equations. All right. So let's substitute equation two into equation one. So equation one tells us X minus Y and in this case, Y is minus two, X, OK equals three. All right. So simplifying we get three, XKX minus minus is going to be plus. So X plus two, X is three, X equals three. And that gives us an X value equal to one. All right. So we've gone ahead, we found our X value. Now, what we wanna do is take that X value and find the corresponding Y value in order to do that, we're gonna substitute into either of our equations. So you can substitute this X value into equation one or equation two. It has to satisfy both. So either one you choose is OK, we're gonna choose to substitute into equation two. Just because it's already the Y is already isolated and we won't need to do any rearranging. OK? So substitute X equals one into equation two. And what we have is Y is equal to minus two times X, which is one, we're just gonna give us Y is equal to minus two. OK? So now we have our X value and our Y value and so we can write our solution set, which is gonna be the 0.1 minus two. So that is our solution and that is going to correspond with answer B I hope this video helped. Thanks everyone for watching. See you in the next one.

In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x

Key Concepts

System of Linear Equations

Substitution Method

Solving Linear Equations

Watch next