In Exercises 63–68, find the solution set for each system by grap...

Question

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

x = y^2 - 3
x = y^2 - 3y

Accepted Answer

By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution. Now, to solve this, we need to find where these two graphs intersect each other. And there's four possible answers with four different graphs. Now we notice here, both graphs will be pointing upwards because both graphs have a positive high degree or in other words, the coefficient on the X squared is positive. So both graphs are pointing up. So now we need to find the intersection point to do this, we can set the two equations equals to each other and solve for X. You have X squared plus 11 equals X squared minus 11. X. Let's solve for X, we can subtract X squared from both sides to get 11 equals negative 11 X. Now let's divide both sides by negative 11 to get X equals negative one. So at X equals negative one, we should have an intersection. Let's check by plugging in X equals N of one into both equations. Y equals X squared plus 11 gives us Y equals N of one squared plus 11 which gives us Y equals 12. For our other value we get why equals X squared minus 11 X which is negative one squared minus 11 times negative one which gives us Y equals one plus 11 or 12. We notice we have the same Y for both of them, Y is equals to 12. This means the solution to our problem happens at negative one 12. So we need a graph that has a solution negative one and 12 and points upwards. And if we look at our possible answers, this makes sense to our problem answer. B OK. I hope they help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. x = y^2 - 3 x = y^2 - 3y