Use elimination method for solving the following equations:
$100x + 200y = 700,200x + 100y = 800$

Hint: When we have two equations to solve by the Elimination method, the first step is to make one of the coefficients of the both equations equal by multiplying with the proper number to the equation.
Then add or subtract according to their sign to eliminate one variable and find the value of another variable.

Complete step-by-step answer:
We have two equations:
$100x + 200y = 700 - - - (1)$
$200x + 100y = 800 - - - (2)$
Make the coefficient of ‘x’ equal in both equations by multiplying equation (1) by 2.
We get:
$200x + 400y = 1400 - - - (3)$
Now subtract equation (2) from equation (3); we get
$400y - 100y = 1400 - 800$
On simplifying;
$ \Rightarrow 300y = 600$
$ \Rightarrow y = 2$
Put vale of $y = 2$ in equation (1);
$ \Rightarrow 100x + 200(2) = 700$
$ \Rightarrow 100x = 300$
$ \Rightarrow x = 3$
Hence the values of variables are $x = 3,y = 2$.

Note: Identifying which coefficient should make equal in the given two equations is the crucial part of this method. For that, carefully check both equations before starting solving the problem.
Usually, our target is to make LCM of numbers which we want to make equal, like in the given question we have 100 and 200 as coefficients of ‘x’ and LCM of 100 and 200 is 200, so our target is to make 200 both numbers by multiplying proper numbers. Try to do minimum calculations as possible.
Another methods to solve pairs of linear equations are substitution method, cross multiplication method etc..