Simultaneous equation?

Can someone tell me how to do this:

3x - 4y =2
xy = 2

Thanks :)

Answers:
First, put one equation in terms of a single variable

xy=2
y=2/x

Then plug this into the other equation:
3x-4y=2
3x-4(2/x)=2
3x-8/x=2
3x^2-8=2x
3x^2-2x-8=0

Then solve the quadratic!
you can take the second on and say
x = 2/y
put that into first one

3(2/y) - 4y = 2
6-4y^2 = 2y
4y^2+2y-6=0
2y^2+y-6 = 0
2y^2+4y-3y-6 = 0
(2y-3)(y+2)=0
y = 3/2 or -2
put both numbers into x=2/y and you'll have your answer
1) 3x - 4y = 2
2) xy = 2

Solve either equation for one of the variables in terms of the other and substitute that result into the other equation.

2) xy = 2
x = 2/y

1) 3x - 4y = 2
3(2/y) - 4y = 2
6/y - 4y = 2
6 - 4y^2 = 2y {multiply by y}
-4y^2 - 2y + 6 = 0
4y^2 + 2y - 6 = 0 {multiply by -1}
(2y + 3)(2y - 2) = 0 {factor}
y = - 3/2, 1

2) xy = 2
x(-3/2) = 2
-3x/2 = 2
-3x = 4
x = -4/3 {when y = -3/2, x = -4/3}

x(1) = 2
x = 2 {when y = 1, x = 2}

Check
1)3x - 4y = 2
3(-4/3) - 4(-3/2) = 2
- 12/3 + 12/2 = 2
- 4 + 6 = 2
2 = 2

3(2) - 4(1 = 2
6 - 4 = 2
2 = 2
Try to solve it like this:

Multiply the first equation 3x - 4y = 2 with y
i.e. y (3x - 4y) = 2y
3xy - 4y*y = 2y
because xy = 2 replace xy in the previous step with 2
i.e. 3*2 - 4y*y = 2y
divide the equation by 2 on both sides and
rearrange the equation as 2y*y + y - 3 = 0
and solve it for quadratic expression

The solution for y = 1 or 3/2
Simple.
write y in terms of x
4y=3x-2
y=.75x-.5
substitute in the second eqn.
x*y=2
[.75x-.5]=2
multiply all terms by 4
3x-2=8
3x=10
x=10/3
y=.75x-.5
=2.5-.5
=2
verify
3[10/3]-4*2
=10-8
=2
ok
3x is wild so teeter the first value and fulimburate the negative 4y into the amassed trunkation and if all is well you will have made a 2 gramme nugget of a silver/gold alloy which is one of the best roofing materials known to man.
issac newton could have made a lot of money in the roofing game after he discovered this but decided to devote his life to solving crummy equations that nobody else could understand.
3x - 4y =2...(1)
xy = 2.....(2)

from (2)

x=2/y

substitute into (1)

6/y-4y=2
6-4y^2-2y=0
2y^2+y-3=0
using quadratic formula
y= {-1+or- sqrt(25}/4
y= -3/2 or 1

go back to (2)

when y= -3/2,x= -4/3
when y=1, x=2

i hope that this helps
3x - 4y =2
xy = 2
y= 2/x
3x- 4(2/x)=2
3x-8/x=2
2x=3x-8
-x=-8
x=8
y=1/4

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