Exercises 86–88 will help you prepare for the material covered...

Question

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

Accepted Answer

Hello Today we're going to be determining whether the give an ordered pair satisfies the equations or not. So notice that we have the same ordered pair for both of the given equations. So we're going to be testing out whether the 0.3 comma negative two satisfies both of our equations. Now in order to determine this, what we're going to do is directly take are given values and plug them in to each equation. And if it makes both equations true then it's going to satisfy both of the equations but sometimes it may not satisfy. So let's just go ahead and plug these in. So recall that we have an ordered pair and an ordered pair is of the form X comma Y. So here X is going to equal to three and y is going to equal to negative two and we're gonna go ahead and plug this in to equation one equation one is three, X plus two, Y is equal to five and substituting in X and Y is going to give us three times three plus two times negative two and that should equal to five. Three times three gives us nine and two times negative two is going to give us negative four and that should equal to five and nine minus four is going to give us five and it is true that that is equal to five. So the current point given to us satisfies the first equation. Now we need to go ahead and check whether it satisfies the second equation. The second equation is seven X plus five X is equal to 11. Now notice that both of the variables are X. So we're gonna replace both of our variables with three. Doing this is going to give us seven times three plus five times three and that should equal to 11. seven times 3 is going to give us 21 And five times three is going to give us 15 and that should equal to 11. Well, 23 plus 15 Is going to give us 38 And 38 is not equal to 11. So the point given to us doesn't satisfy the second equation or in other words, it's true for the first equation but not true for the second equation. And that means that the answer to this problem is going to be B. So I hope this video helps you in understanding how to determine whether an ordered pair satisfies the corresponding equations and I'll go ahead and see you all in the next video.

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

Key Concepts

Ordered Pairs and Coordinates

Substitution in Equations

Linear Equations in Two Variables

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