System of equations help?

Question

4/x - 3/y = 8
5/x - 8/y = 13

I usually excel in math. I understand systems but I didn't understand how to solve this one. I just want to understand the process by which to do this, so help and explanation will be extremely appreciated.

Answer 1

Solve for x in terms of y, then plug that into the second equation and solve for x. then plug in the value for x and find y.

4/x - 3/y = 8

4/x= 8 +3/y multiply both sides by x
(4/x)x = x(8+3/y) simplify and get x by itself
4/(8+3/y) = x

Plug this into the second equation

5/(4/[8+3y]) - 8/y = 13 solve for y

etc...

Answer 2

the place to start is to discover a thank you to combine the two equations into one ideally eliminating between the unknowns interior the approach. So: x-y=3 might properly be rearranged to x=3+y Substituting this into the 1st equation provides (3+y)squared + y squared = 29 remedy this to get an answer for y then replace this selection for y interior the 2nd equation and remedy to get x. answer: y = 2 x = 5

Answer 3

Or you could get tricky and multiply through by xy before you start to get rid of the fractions:

(4/x - 3/y = 8 => 4y-3x=8xy)
(5/x-8/y = 13 => 5y-8x=13xy)

You'll be able to cancel out the xy's pretty early on, too.

Answer 4

Start by multiplying each equation by xy...

4y - 3x =8xy and 5y - 8x = 13xy

Rearranging the 1st equaton we have...

4y = x(3+8y) and so x = 4y/(3+8y)

substitute this expression for x into the second equation...

5y - 32y/(3+8y) = 52y^2/(3+8y)

Multiplying throughout by (3+8y) and collecting terms we have

12y^2 + 17y = 0 so either y=0 (impossible because of division by zero) or y = -17/12

Substitute this value of y into any of the equations and get x.

Answer 5

use substitution.

go like:

4-3/y=8x

x= 4/8-3/y/8

x= 1/2-24/y

then you would put it in the other one

5/(1/2-24/y) =13

it might be easier to do y= or something, but yeah :)


there is always a chance im wrong, havent done this stuff in a really long time lol.. but that is HOW you do it, just not sure if all my math is correct

Answer 6

let a = 1/x and b = 1 / y
4a - 3b = 8
5a - 8b = 13

-20a + 15b = - 40
20a - 32b = 52------ADD
- 17b = 12
b = - 12/17

4a + 36/17 = 8
4a = 136/17 - 36/17
4a = 100/17
a = 25/17

x = 17/25 , y = - 17/12

Answer 7

multiply both sides of both equations by xy.
4y-3x=8xy -- (1) or 4y-8xy=3x
5y-8x=13xy -- (2)
4y(1-2x)=3x from (1)
y=3x/4(1-2x)
put this y in (2)
5[3x/4(1-2x)]-8x=13x[3x/4(1-2x)]
15x/4(1-2x)-8x=13x/4(1-2x)
multiply both sides by 4(1-2x)
15x-8x(4)(1-2x)=13x
15x-32x+16x^2-13x=0
16x^2-30x=0
x(16x-30)=0
x=0
16x=30
x=30/16=15/8
put this x in (1) and solve for y.