solve the simultaneous equation 3x/y+4y/x+8=0 and 2y=x-4?

Question

please show me step by step cos i am new to this type of question. thank you

32y^2 + 80y +48 = 0
(2y+3)(2y+2) = 0

can someone tell me how to factorize ? tq

Answer 1

the solution is:
(3x-2)/2y + (4y)/x +8=0,
(6x)/(x-4) +2(x-4)/x + 8=0,
"6xsq +2(xsq - 8x +16)"/x(x-4) +8=0,
6xsq+2xsq-16x+32+8x(x-4)=0,
8xsq-16x+32+8xsq-32x=0,
16xsq-48x+32=0,
xsq-3x+2=0,
x=1,x=2 eseq.
(the above xsq mean x power of 2).

best wishes n happy new year.

Answer 2

First step -- isolate one of the variables. In this case, add 3/y to both sides of the lower equation. This leaves you with that equation reading 1/x = 3/2 + 3/y. Invert both sides, leaving x = 1/(3/2 + 3/y). Plug this value for x into the top equation, which then becomes 4/(1/(3/2 + 3/y)) + 1/y = 5/3. But 1/(1/(3/2 + 3/y)) = 3/2 + 3/y, so multiplying this by 4 gives 12/2 + 12/y + 1/y = 5/3. Putting all of the y's on one side and all of the numbers on the other gives 12/y + 1/y = 5/3 - 12/2. adding these gives 13/y = (-6+5/3) = -18/3 + 5/3 = -13/3. Thus y = -3. Plugging this value for y into the top equation yields 4/x + 1/(-3) = 5/3 adding 1/3 to each side yields 4/x = 5/3 + 1/3 . or 6/3, or 2. Since 4/x = 2, x must equal 2. Checking, using both values, 4/2 + 1/(-3) = 5/3, and 2 - 1/3 = 5/3 1/2 -(3/-3) = 3/2, and 1/2 + 1 = 2.

Answer 3

2y = x-4
x = 2y+4


3x/y + 4y/x + 8 = 0
multiply xy
----> 3x^2 + 4y^2 + 8xy = 0
3(2y+4)^2 + 4y^2 + 8(2y+4)y = 0
3(4y^2 + 16y + 16) + 4y^2 + 8(2y^2 +4y) = 0
12y^2 + 48y + 48 + 4y^2 + 16y^2 + 32y = 0
32y^2 + 80y +48 = 0
(2y+3)(2y+2) = 0
y = -3/2 y = -1

Answer 4

3x/y+4y/x+8=0(1) and 2y=x-4
let t = x/y <=> x = yt ; t <> 0
(1) <=> 3t + 4/t + 8 = 0
<=> 3t^2 + 8t + 4 = 0
<=> t = -2/3 or t = -2

t = -2/3 :
we have
3x = -2y
2y = x - 4
=> x = 1 y = -3/2

t = -2
we have
x = -2y
2y = x - 4
=> x = 2 y = -1

Answer 5

1.x=2y+4
2. We put this new x in 3x/y+4y/x+8=0
3(2y+4)/y+4y/(2y+4)+8=0
3.(6y+12)(2y+4)+4yy=-16yy-32y
4. 12yy+24y+24y+48+4yy+16yy+32y=0
5. 32yy+80y=-48
6. y=-3 x=-2

Answer 6

i think it is not complete statement or is it from integration only thing that wold help is some formulae or theory.all d best if it is ur home work or test.

Answer 7

Doin' some homework, honey?

Answer 8

minus 24x plus five y

Answer 9

Isn't this YOUR homework?