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. (2,−1, 3) x+  y+0z=4, x−2y−0z=1, 2x−y−2z=−1

Accepted Answer

Hello Today we're going to verify whether the order triplet satisfies the system of equations. So the order triplet given to us is one comma negative one comma two and recall that the form of every order triplet is of X comma Y comma Z. So the substitution for X is going to be one. The substitution for why it's going to be negative one and the substitution for Z is going to be too. So in order to verify whether this satisfies the equation or not, we need to go ahead and plug in these values to all three of our given equations. And if it makes every equation true then the order triplets satisfies the system of equations. So let's just go ahead and start by plugging in these values into equation one, equation one is x plus y plus Z is equal to two, X is one. So we have one plus Y which is negative one plus Z which is two and that should equal to two plus negative one is just going to be minus one. So we can change this to one minus one plus two and one minus one is just going to give us zero and zero plus two is going to give us too. So we have two is equal to two which is a true statement. So it satisfies the first equation. Now we want to go ahead and repeat this process for equations two and three, equation two is two, X minus Y is equal to three, two times X is just gonna be two times one minus Y which is negative one. And that should be equal to three minus negative one is just going to be positive one. So we can change this to two times one. Plus one should equal to 32 times one is just going to give us two plus one is going to give us three. And what we are left with is three is equal to three which is a true statement. So the order triplet satisfies the second equation. The 3rd equation is X -3, Y -2, Z is equal to zero. Now again we're going to make the substitution so X is one minus three times Y which is negative one minus two times E, which is two. And that should equal to zero, three negative three times negative one is going to give us positive three. So we have one plus three minus two times two which is four and that should give us 01 plus three, is going to give us four And 4 - gives us zero. So we have zero is equal to zero, which is a true statement. And since all three of the equations are true, that means that the order triplet does satisfy the system of equations. So the answer to this problem is going to be a so I hope this video helps you understanding how to perform this process and I'll go ahead and see you all in the next video

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In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+ y+0z=4, x−2y−0z=1, 2x−y−2z=−1