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).

2x + y = 1

x² + y² = 10

Accepted Answer

Hello everybody. Everything. All right today that we're going to be looking at this question that states out of two solutions of the given nonlinear system, one solution is, and they give us kind of like a set of points. Hello, everybody. I I today that we're going to be looking at this question that states out of two solutions of the given nonlinear system, one solution is open parentheses, blank comma two closed parentheses. So they're giving us the Y component of the solution. And the nonlinear system includes equation number one, which will be two X plus Y equals eight, an equation number two which will be X squared plus Y squared equals 13. Now the S provided are a negative 30 B zero C three and D nine. Now for a question like this where they gave us two different equations and they gave us the Y component of our answer. The quickest route to take here would be to simply plug, plug in that Y for our equations and see what the solution would be and see if it matches up. So if we have a Y of two in equation number one, we'll have that two X plus Y equals eight. So two X plus two equals eight, and then we move the two from the left hand side to the right hand side by subtracting. So we have two, X equals six or X equals three. And that means that if we have a Y of two, our X will be equal to three. Now, we can confirm that by doing the same thing with equation two. So we'll have X squared plus Y squared equals 13. And if we plug in our Y of two, we'll have X squared plus two squared equals 13. And that means X squared plus two, squared is four. So we'll have X squared plus four equals 13. And now we can move the four over from the left hand side to the right hand side. And we'll have X squared is equal to a 13 minus four which is nine. And finally, we'll have that X is equal to plus or minus three. However, if we plug in the negative three as one of our answers, it won't work as a correct answer. So if we plug in negative three and let's just test it. If X equals negative three, what I said with the equation one, then equation one will be two multiplied by negative three plus two, which was A Y that will be equal to +82, multiplied by negative three is negative six plus two equals eight. And then we'll have that negative six plus two is negative four and negative four does not equal eight. Therefore, X equals negative three is not possible. So X equals positive three and cannot be negative three. Or in this case, answer choice C 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).
2x + y = 1
x² + y² = 10

Key Concepts

Solving Systems of Equations

Substitution Method

Nonlinear Equations and Circles

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