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

Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)? 
x^2 + y = 2 (1) 
x - y = 0 (2)

Accepted Answer

Hello everybody. I have everything. All right. Today today we're going to be looking at this math question that states what is the resulting equation when we substitute the solution for Y in equation two into equation one to solve the given nonlinear system using the substitution method. Now equation one is X squared plus two, Y equals 63. An equation two is X minus Y equals zero. Now the answer just provided R A X squared plus two, X equals 63 B Y squared plus two, Y equals 63 C X squared minus two X equals 63 N D Y squared minus to Y equals 63. Now this question, when we read it, we see that it's telling us exactly what to do. So we have to substitute the solution for Y in equation two into equation one. So the first thing we have to see is the solution for Y in equation two. So we have to solve for why? So using equation two, we'll have, we can move the X over from the left hand side to the right hand side and we'll have that negative Y is equal to negative X and we don't want to work with the negative here. So we multiply everything by negative one and we'll have that Y is equal to X. So that's our solution for Y in equation two. Now it's telling us to substitute this into equation one. So we're doing exactly that. So in equation one, we had X squared, so that remains the same because it's an X and then we had plus two Y. And now this is where we substitute in the Y that we obtain in equation two. So we have, instead of two Y, we have X squared plus two multiplied by the Y that we got, which was X. So we'll have X word plus two, X equals 63. And that would be it. We solved the Y in equation two and we use that information to substitute it in equation one. And this is the equation that we obtain X squared plus two, X equals 63 or in this case, answer choice A. So I hope that was helpful. And until the next time.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing