In Exercises 19–30, solve each system by the addition method.

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Question

In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3

Exercise 19: Solve the system of equations x + y = 1 and x - y = 3 using the addition method.

Accepted Answer

everyone welcome back in this problem. We are asked to solve the given system of equations using the addition method. Okay, the equations were given us five X plus Y equals seven and five X minus Y equals 13. Okay, so we're just going to rewrite our equations five X plus Y equals seven. We're going to label them. So we'll call this equation one and then we have five X minus Y equals 13. We'll call this equation to Okay, that just makes it easier for referring to them later on. All right now we're told to use the addition method were called The addition method tells us to add the two equations together in case we have five X plus five X. That gives us 10 X. We have plus Y plus negative Y. Well that's just gonna be zero and seven plus 13 is going to give us 20 on the right hand side. And what you'll see is that now we have just an equation of X. Ok, so we can solve for X. We've eliminated Y. Ok. And sometimes you'll see in textbooks the addition method be referred to as the elimination method. Okay, And that's why we're kind of eliminating one of those variables. Alright, so if we divide each side by 10, we get X is equal to two. Okay, so we have our x value that we're looking for here. Alright, now we need to substitute that X value into one of our equations to find the corresponding why that Okay, we can choose either equation. In this case we're going to choose um equation one. So let's sub X equals two into equation one. Okay. And this is where it's handy to have labeled those equations. So we're gonna have five times two plus Y equals seven, expanding 10 plus Y is equal to seven and moving 10 to the right hand side. We have Y is equal to minus three. Okay? So now we have an X. Value and a corresponding y value. We just need to write the solution set. So the solution in this case is gonna be one single point. It's gonna be 2 -3. So there's our solution that's gonna correspond with solution be that's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3

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