In Exercises 29–42, solve each system by the method of your choic...

Question

In Exercises 29–42, solve each system by the method of your choice. x^3+y=0, x^2−y=0

Accepted Answer

Welcome back. I am so glad you're here. We are given the system of equations. The first equation is y cubed minus X equals zero and the second equation is X plus two, Y squared equals zero. We are asked to solve this system of equations. Well I'm going to solve it using substitution, I'm going to subtract two y squared from both sides of the second equation so that I'll have X by itself that will read X equals negative two Y squared. And now where I have an X. In the first equation I can substitute this negative two y squared. So the first equation will read three or excuse me, Y cubed minus parentheses negative two, Y squared and parentheses equals zero. And I put that in parentheses to note that we have a minus a negative which simplifies to a plus. So it's now y cubed plus two, I squared equals zero. And both of those two terms on the left hand side have a Y squared in them. So I'll factor that out. And inside the parentheses that will leave Y plus two, not all equal zero. And now I have two factors, I can set them both equal to zero, Y squared equals zero and y plus two equals zero. And I can solve for y. First one take the square root of both sides. And that gives me Y equals well the square root of zero is zero and plus or minus zero is just zero. So this is just Y equals zero. For the second one. I can subtract two from both sides and I get why equals -2. So I have two solutions for why I can create a solution set and fill in my Y values that I know. So I know one solution for Y is zero and the other that I know is negative two. And now I can choose either formula. I'm going to choose the second equation X plus two, Y squared equals zero. I'll write it two times because I have two Y values to fill in. And as I fill in the Y values I can solve for X. So when Y equals zero I can plug that in here and I'll have X plus two times zero squared equals +00 squared +02 times zero is zero. So this is just X equals zero. So when y equals zero, X also equals zero. There's my first ordered pair and now I'll plug this negative two in for Y. So that I can find out my X value. When y equals negative two. Well -2 squared is a positive four And two times 4 is eight. And subtracting eight from both sides to get X by itself, we get X equals negative eight. So when y equals negative two, X equals negative eight. I look at my answer choices and this matches with answer choice. D Well done, we'll catch you on the next one

In Exercises 29–42, solve each system by the method of your choice. x^3+y=0, x^2−y=0

Key Concepts

Systems of Equations

Substitution Method

Graphical Interpretation

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