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cutiecomittee123
 one year ago
Help me
Solve this system of equations to get the sum of all of the x coordinates from the solutions.
x^2+4y^2=100
4yx^2=20
cutiecomittee123
 one year ago
Help me Solve this system of equations to get the sum of all of the x coordinates from the solutions. x^2+4y^2=100 4yx^2=20

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you posted this question earlier

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Im pretty sure it was involving different equations

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The one from before were different equations. But the same idea holds. You want to make some sort of substitution that will let you reduce one of the equations to only x or only y. So you're looking for something in common in both equations that will make for an easy substitution. I see that both equations have an x^2 term. So if I were to solve the first equation for x^2, I would get x^2 = 100  4y^2 With me so far?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Yes I am with ya

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0wait wouldnt you get 4y^2+4y=80 because you can cancel out the two x^2's since one is negative and if you add the equations it works right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, if we do the substitution for x^2 into the 2nd equation. we get 4y  (1004y^2) = 20 4y  100 + 4y^2 = 20 4y^2 + 4y = 80 SO yes, you're right, good job :) Would you know what to do from here?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Now move 80 to the other side and you get 4y^2+4y80=0 Then factor

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0thats where I get confused because what adds to get 4 but multiplies to get 80???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, conveniently all of those terms are divisible by 4, so let's just divide out the 4 from all terms. Doing this would reduce the quadratic into y^2 + y  20 = 0

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0thats a lot cleaner and easier to deal with

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, how does that factor?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, 20 would need to factor into 2 numbers that would also add up to a positive 1. This means: One of the numbers has to be positive and the other has to be negative (otherwise they would never multiply to a negative 20) The largest of those 2 numbers must be positive. So can you come up with the two numbers? Two factors that multiply to 20 yet add to positive 1

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0no, I bet its really easy but I just cant wrap my head around it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is easy. And youll think its easy also once you get used to the process. Okay, so let's look at how 20 could possibly break apart: dw:1433533847258:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So those are the possible combinations we need to consider. Now, in order for any of those 2 numbers to add to a positive value, the largest one must be positive. Thus we can more specifically consider these 3 choices: dw:1433533919775:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And yeah, you got it, haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Correct :) Now since y must be either of those values, you can substitute each one into one of your given equations and solve for x

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.05 doesnt work when plugged in so its got to be 4

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0After plugging in 4 to the equation I get x=6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How does it not work?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which just means x = 0

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0x^2+4(5)^2=100 x^2+100=100 100 100 x^2=0 but you cannot take the square root of 0

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Like how does that work?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0nevermind. so now we know that (4,6) is a solution, Next we have (0, and we have to solve for the y coordinate right?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Wait no its just (0, 5)

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0So since there are only 2 intersections right? its safe to go ahead and add up the x coordinates. which are; 4 and 0. So the answer is 4 as the sum of all x coordinates for the solutions/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0SOrry for the late response. But yeah, the square root of 0 is just 0. So you get the coordinate point (0,5) as mentioned. Now when you plug in y = 4 however, we have to be a bit more careful. Let me plug y = 4 into the 1st equation: x^2 + 4(4)^2 = 100 x^2 + 64 = 100 x^2 = 36 Now at this point, need to remember that when we square root both sides of an equation, we need to use a plus or minus. So we actually have x = 6 and x = 6

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Currently plugging that into the first equatiom

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0So final answers are (4,6) (0,5) (6,4) (6,4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So we actually have 3 solutions. dw:1433534800787:dw Sorry for the bad drawing, but yeah.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember, we found y = 5 and y = 4. Using y = 5, we got x = 0 and only x = 0. So that means the coordinate is (0, 5). Now we have y= 4. We plugged that in and got 2 xvalues, 6 and 6. Now be careful, these are xvalues, gotta put the coordinates in the correct order. This gives us the two coordinates (6,4), (6,4) So 3 solutions total and the graph above shows the 3 intersections.

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.0Okay so we only use the solutions (0,5), (6,4), and (6,4) Which gives a sum of 0 for the x coordinates
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