what is x/y if (3x-y)/(x+y)=4/7 is true?

Question

I’m so lost here. I don’t know whether to solve the equation for one variable or both but they will still be in terms of the other. What does them being true mean to me?

Answer 1

(3x-y)/(x+y)=4/7

3x-y=4

x+y=7

3x-y=4 implies y=3x-4

substitute

x+(3x-4)=7

4x-4=7

4x=11

x=2.75

y=7-2.75

y=4.25

check:

[3(2.75)-4.25]/(2.75+4.25)=

[8.25-4.25]/(2.75+4.25)=

4/7

so x=2.75 and y=4.25

x/y=2.75/4.25

x/y=275/425

x/y=11/17

or...

cross multiply

4(x+y)=7(3x-y)

4x+4y=21x-7y

7y+4y=21x-4x

11y=17x

divide both sides by y and then by 17

11/17=x/y answer again

Answer 2

(3x-y) / (x+y) = 4/7

4(x+y) = 7(3x-y)

4x + 4y = 21x - 7y

17x = 11y

So, x/y = 11/17