In Exercises 1–4, determine if the given ordered triple is a solu...

Question

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

Accepted Answer

Hello Today we're going to be verifying whether the ordered pair given to us satisfies the system of equations. Now, in order to check this, we need to go ahead and take the values of the order pair given to us and plug into each of our equations. And if these values make all three of the equations true then it verifies that this is a solution to the system of equations. So the ordered pair given to us is three comma one comma seven. Now this is an order pair of three variables. So this is of the form X comma Y comma Z. And let's go ahead and plug in our values into equation one, equation one is two, X minus Y is equal to five, X is three and y is one. So plugging in these substitution is going to give us two times three minus y, which is one equal to 52 times three is going to give us six. So we have six minus one is equal to five and six minus one is going to give us five. So what we are left with is five is equal to five and that is a true statement. So the order triplet satisfies equation one Now we want to go ahead and repeat this process for equation to an equation three, equation two is four, X plus Y is equal to 13. Plugging in for X is going to give us four times plus y which is one and that should equal to 13. 4 times three is going to give us 12 plus one is equal to 13 and 12 plus one is going to give us 13. So what we are left with, if this is 13 equal to 13 and that is a true statement. Now let's go ahead and check equation three, equation three is three, y minus two. Z is equal to negative 11. three times why? or three times 1 minus two times E or two times seven should equal to negative 11. 3 times one is going to give us three and negative two times seven is going to give us negative 14 and 3 -14 is going to give us negative 11 And that is also going to be equal to negative 11, which is a true statement. So since our order triplet satisfies all three equations, that means that this is a solution to the system of equations. So the answer to this problem is going to be a So I hope this video helps you in understanding how to do this process and I'll go ahead and see you all in the next video.

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

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