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cutiecomittee123
 one year ago
Solve this system of conic section equations
7y^2+x^2=64
x+y=4
cutiecomittee123
 one year ago
Solve this system of conic section equations 7y^2+x^2=64 x+y=4

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3First solve the equation x+y = 4 for y \[\Large x+y=4\] \[\Large y=4x\] Now plug this into the other equation so you boil things down to one variable only \[\Large 7y^2+x^2=64\] \[\Large 7(4x)^2+x^2=64\] \[\Large 7(168x+x^2)+x^2=64\] \[\Large 11256x+7x^2+x^2=64\] \[\Large 11256x+8x^2=64\] \[\Large 11256x+8x^264=0\] \[\Large 8x^256x+48=0\] From this point, you need to solve for x. To do so, I recommend using the quadratic formula. I'll let you do this part. Tell me what x values you get as the solutions.

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1I get x=1 and x=6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3if x = 1, then y = ???

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1sweet and then just plug that into on of the original equations to solve for y

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3yes or plug into y = 4x since that already has y isolated

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1so like y=41 and y=46

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3correct, so the solutions are these two ordered pairs (1,3) and (6,2) and this confirms it http://www.wolframalpha.com/input/?i=7y^2%2Bx^2%3D64%2Cx%2By%3D4

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1wanna help me with another one?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3what's your question?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1x^2+y^2+2x+2y=0 x^2+y^2+4x+6y+12=0 solve this system of equations

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3ok at first this looks really complicated, but we can eliminate quite a bit here notice how each equation has x^2+y^2 in it so we can subtract the equations (either equation1  equation2 or equation2equation1) to eliminate the x^2+y^2 terms what do you get when you subtract?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3Now let's solve 2x+4y+12=0 for x 2x+4y+12=0 2x+4y+1212=012 2x+4y = 12 2x+4y4y = 12  4y 2x = 4y  12 2x/2 = (4y12)/2 x = 2y  6

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1now plug that into the other equation

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3Next, plug x = 2y  6 into either original equation. I'll pick the first equation x^2+y^2+2x+2y=0 (2y6)^2+y^2+2(2y6)+2y=0 ... replace x with 2y6 (4y^2+24y+36)+y^2+2(2y6)+2y=0 4y^2+24y+36+y^24y+12+2y=0 5y^2+22y+48=0 solve that for y (use the quadratic formula). Tell me what you get

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3hmm I messed up, let me fix

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3x^2+y^2+2x+2y=0 (2y6)^2+y^2+2(2y6)+2y=0 ... replace x with 2y6 (4y^2+24y+36)+y^2+2(2y6)+2y=0 4y^2+24y+36+y^24y12+2y=0 ... it should be 12, not +12 5y^2+22y+24=0

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1well I tried and I got the b^24(a)(c) = 476 you cant take a square root of a negative number

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3I fixed my mistake and got 5y^2+22y+24=0

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1oh gotcha let me try that

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1y=2 and y=2.4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.32.4 or 12/5

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3now use each y value to find the corresponding x value

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.112/5? how did you get that?

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.122+ or = the sqrt of 4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3I used the quadratic formula or you can convert 2.4 to fraction form 2.4 = 2.4*(10/10) = 24/10 = 12/5

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1so now we plug in the y values to get x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3you can use x = 2y  6

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1x=10.8 and x=10

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3incorrect on both

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3if y = 2, then x = 2y  6 x = 2(2)  6 x = 4  6 x = 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3if y = 2.4, then x = 2y  6 x = 2(2.4)  6 x = 4.8  6 x = 1.2

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1so the solutions are (2,2) and (1.2, 12/

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3correct and the graph confirms it

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3I think you meant to say 12/5

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3if you use 12/5 then convert 1.2 to fraction form as well 1.2 = 1.2*(10/10) = 12/10 = 6/5

cutiecomittee123
 one year ago
Best ResponseYou've already chosen the best response.1Yeah I did mean 12/5 thanks:))
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