Completing the following equation by the suitable method i got this linear equation two variable problems for my school.
I understand the basics of the normal linear equation but this seems different instead having a pure number after the "=" they got a ration, here is the problem.
$$X:2Y = 5:14$$
$$(X+4) : (3Y-21) = 2:3$$
What i've tried to do is just guess the X and Y and to solve it (took a long time and still dont find it) so as example if the X is 5 and the Y is 7, it fit the first equation but wont fit in the 2nd question.
The ":" sign is for ration, not "divided by"
Please answer how you solve and not just give the answer, because as you see im trying to learn not trying to just solve my homework.

We can start by solving both equations for the same variable.
$$X:2Y = 5:14\implies Y = \frac{7 X}{5}$$
$$(X+4) : (3Y-21) = 2:3 \implies Y = \frac{X + 18}{2}$$
We now equate the two "solutions" of $Y$.
$$\frac{7 X}{5}=\frac{X + 18}{2}\\
\implies \frac{7 X}{5} = \frac{X}{2} + 9\\\implies 14X-5X  =90\\
\implies X=10\qquad
\implies  Y=\frac{7 X}{5}
=\frac{70}{5}=14$$
