SOLUTION: Solve the system by elimination or substitution. 3y^2=xy 2x^2+xy-84=0

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Question 919862: Solve the system by elimination or substitution.
3y^2=xy
2x^2+xy-84=0
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
3y%5E2=xy .........eq.1
2x%5E2%2Bxy-84=0.....eq.2
_______________________________

3y%5Ecross%282%29=xcross%28y%29 .........eq.1

3y=x ......substitute in eq.2

2%283y%29%5E2%2B%283y%29y-84=0.....eq.2
2%289y%5E2%29%2B3y%5E2-84=0
18y%5E2%2B3y%5E2-84=0
21y%5E2=84
y%5E2=84%2F21
y%5E2=4
y=sqrt%284%29
y=2 or y=-2
go to 3y=x, plug in 2 for y
3%2A2=x
x=6
now plug in -2 for y
3%2A%28-2%29=x
x=-6
so, solutions are:
x=6 and y=2
or
x=-6 and y=-2

+graph%28+600%2C+600%2C+-50%2C50%2C+-70%2C+70%2C+x%2F3%2C+-2x%2B84%2Fx%29+

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute for xy in the second equation, and at least you can find a relationship between x and y. Then try to work with this and what you believe to be the simpler equation....

2x^2+3y^2=84, does not look useful.



INSTEAD, DO THIS WAY:
Solve for x in terms of y from....
...
x=%283y%5E2%29%2Fy
-
2%283y%29%5E2%2Bxy-84=0
2%283y%29%5E2%2B3y%5E2-84=0, includes substitution for xy.
18y%5E2%2B3y%5E2=84
21y%5E2=84
y%5E2=4
highlight%28y=-2%29 or highlight%28y=2%29.

Find each corresponding value for each y just found.
x=3%2A%28-2%29%5E2%2F%28-2%29
highlight%28x=-6%29 when highlight%28y=-2%29
-
x=3%282%29%5E2%2F2
highlight%28x=6%29 when highlight%28y=2%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the system by elimination or substitution.
3y^2=xy
2x^2+xy-84=0


Solve the system by elimination or substitution.

3y%5E2+=+xy______x+=+3y%5E2%2Fy______x+=+3y ------ eq (i)

2x%5E2+%2B+xy+-+84+=+0 ------ eq (ii)

2%283y%29%5E2+%2B+y%283y%29+-+84+=+0 -------- Substituting 3y for x in eq (ii)

2%289y%5E2%29+%2B+3y%5E2+-+84+=+0

18y%5E2+%2B+3y%5E2+-+84+=+0

21y%5E2+-+84+=+0

21%28y%5E2+-+4%29+=+21%280%29

y%5E2+-+4+=+0_____y+=+0+%2B-sqrt%284%29________highlight_green%28y+=+0%2B-2%29

x+=+3%282%29 -------- Substituting 2 for y in eq (i)

highlight_green%28x+=+6%29

highlight_green%28highlight_green%28system%28x+=+6_when%2Cy+=+2%29%29%29



x+=+3%28-+2%29 ------ Substituting - 2 for y in eq (i)

highlight_green%28x+=+-+6%29

highlight_green%28highlight_green%28system%28x+=+-+6_when%2Cy+=+-+2%29%29%29