Question

If x +3y =6 and 2x-y =3, then x/y=?

Answer 1

x+3y=6......(1)
2x-y=3.....(2)

by elimination method

multiply equation (1)by2 and equation(2)by1
2(x+3y=6) =2x+6y=12(3)
1(2x-y=3) = 2x-y =3(4)
now subtract equation (3) by (4)
2x+6y=12
2x - y=3
(-) (+) (-)

0+7y=9
y=9/7

now put this value in equation (2)

2x-y=3
2x-9/7 = 3
2x = 3+9/7
2x= 21+9/7
x= 30/7×2
x=30/14
x=15/7

now A.T.Q

x/y = ?
= 15/7/9/7
= 15/9


answer = 15/9

Answer 2

Hey There!

Here we can solve the question as follows:

$x+3y=6 \\ \\ \text{Dividing by y} \\ \\ \implies \frac{x}{y} + 3 = \frac{6}{y} -----(1)$


Now,

$2x-y=3 \\ \\ \text{Dividing by y} \\ \\ 2\frac{x}{y} - 1 = \frac{3}{y} -----(2)$


Now, consider first equation again:

$\frac{x}{y}+3 = \frac{6}{y} \\ \\ \\ \implies \frac{x}{y}+3 = 2 \times \frac{3}{y}$

Now, we substitute from second equation:
$\frac{x}{y}+3=2\times ( \frac{2x}{y}-1) \\ \\ \\ \implies \frac{x}{y} + 3 = \frac{4x}{y}-2 \\ \\ \\ \implies \frac{4x}{y} - \frac{x}{y} = 3+2 \\ \\ \\ \implies \frac{3x}{y} = 5 \\ \\ \\ \implies \boxed{\frac{x}{y}=\frac{5}{3}}$


Hope it helps
Purva
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