Answer each of the following. When appropriate, fill in the bl...

Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____).

x + y = 7

x² + y² = 25

Accepted Answer

Hello everybody. And we're doing all right today. So we're going to be looking at this question that states out of two solutions of the given non-linear system, one solution is open parentheses, zero comma blank, close parentheses. So they're giving us the X component of our answer. But, and we're trying to solve for the Y component where our two equations will be, we have equation number one being X plus Y equals nine and equation number two will be X squared plus Y squared equals 81. Now, the answer choice provided are a negative nine B zero C nine and D 81. Now for a question like this where they give me the X component, the easiest route to take is just simply plugging in that X component to our equations to see what the Y component would be. So if we plug it into equation one, we'll have that we had X plus Y equals nine. And now if X equals zero, we have zero plus Y equals nine, which means that Y equals nine. And that means that if we have an X component of zero R Y equals nine, and now we can confirm that with equation number two. So we'll do the same thing. We'll plug in zero for the X and equation two. So we had equation two was X squared plus Y squared equals 81. And then we plug in zero, we have zero squared plus Y squared equals 81. Zero. Squared is zero. So we'll have that Y squared equals 81 which means that Y is equal to plus or minus the square root of 81 which means that Y equals plus or minus nine. So now we got also a Y of nine but the possibility of Y equals negative nine. So we have to test this and we test it back in equation number one. So we have, we'll plug in negative nine A Y of negative nine into our equation number one to see if it works. So we'll have zero plus Y. In this case, our Y is negative nine. So it will be zero minus nine equals nine. The zero can be taken away and we'll have negative nine equals nine, which is not true. So we'll have negative nine does not equal nine. Therefore X equals negative or Y equals since we're solving for why? Here we have Y equals negative nine is not possible. Therefore, once again, Y equals ninth and that means that we have an X component of zero, we have a Y component of positive nine or answers choice D in this question. So I hope that was helpful. And until next time.

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____).
x + y = 7
x² + y² = 25

Key Concepts

Solving Systems of Equations

Substitution Method

Interpreting Solutions of Nonlinear Systems

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