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.

(y - 2)^2 = x + 4
            y = - (1/2)x

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. We have Y minus seven squared equals X plus 19 and Y equals X minus four. Our possible answers are four different graphs and solution sets. Now to solve this, we need to find the points where they intersect where both these equations intersect. To find this, we can substitute our equations. We have Y equals X minus four. Let's go ahead and substitute, let's say we get X minus four minus seven squared equals X plus 19. And we can go ahead and solve for X yeah, X minus 11 squared equals X plus 19. We can go ahead and expand our X minus 11 squared to get X squared minus 22 X plus 1 21. This equals X plus 19. We can now solve for X by saying this both equations equals to zero, subside X and 19 to get X squared minus 23 X +102. Now to solve this, we need to find two numbers that multiply to equal 102 and add to equal to negative 23. If we have 102, we can find a few factors. 11 of the two, two and 51 three and six and 17. You can actually stop there. Now we have a negative 23 X. So both numbers should be negative. Let's say our two numbers are six and 17 and we actually want negative X minus six multiplied by X minus 17 equals zero. Now to find our two X vice, we can set both equal to zero and solve X minus six equals zero, X minus 17 equals zero, giving us X equals six and X equals 17. Now, we have both values. We can plug this into our equation to solve for Y, we can plug it into the second Y equation. Y equals X minus four. We have six minus four which gives us two 17 minus four, which is 13, are two points, then are 62 and 17 13. If we look at our possible answers for this solution set, we determine the answer to our problem. This 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. (y - 2)^2 = x + 4 y = - (1/2)x