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

Question

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

Exercise 21: Solve the system of equations 2x + 3y = 6 and 2x - 3y = 6 using the addition method.

Accepted Answer

everyone in this problem. We are asked to solve the system of equations using the addition method and the system of equations were given here is seven X plus two, Y equals eight and seven x minus two equals 20. So let's just go ahead and rewrite the system that we're given. Okay? And we're gonna label our equations case. We have equation one and equation to this just helps us if we need to refer back to them later on. So the first equation is seven X plus two, Y equals eight and the second equation is seven X coupe minus minus two. I equals 20. Okay, now they were told to use the addition method and sometimes a variation of this can be called the elimination method depending on what textbook you're using. The addition method wants us to add the two equations were given together. And so if we add these equations we have seven X plus seven X. Okay, that's gonna give us 14 X. We have plus two, Y plus minus two, Y is just gonna give us zero. And then on the right hand side eight plus 20 that's going to give us we can see that our equation now just has X terms. It has no Y terms. So we can go ahead and solve for us and that's what the goal of the addition method is. Is to eliminate one of those variables. That's why sometimes it's referred to as the elimination method. Alright so now we have 14 x equals 28. We can divide both sides by 14 and we get X is equal to two. Okay? Alright so we have x equals to two. Now we need to find a corresponding y value. Okay so let's substitute X equals two and we can substitute it into either of our equations. Okay? We're solving the system so both of those equations have to be satisfied. So we can solve sub it into either equation. Let's just go ahead and choose equation one. Okay that's gonna give us seven times to that X value plus two. Y equals eight. Okay so we have 14 plus two. Y equals eight. Subtracting 14 from both sides two Y equals minus six and dividing by two. Y. Is equal to minus three. Okay so we found an X. Value of two and a Y. Value of minus three. That's gonna give us a solution set okay? With a single point and the point is two minus three. Okay so this is our solution here and that is going to correspond with answer A. That's it for this one. Thanks for watching. See you in the next video

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

Key Concepts

System of Linear Equations

Addition Method (Elimination Method)

Solving for Variables After Elimination

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