# Hello i have a doubt in this question for elimination method why are we multiplying 2 to the second equation? and why cant we use other numbers like 3 , 4 , 5 etc.? Solution

Equations are
3x + 6y = 7000 .....(1)
and
2x + 3y = 3855 .....(2)

so if we want to eliminate x from both the equations:

multiply eq(1) by 2 (i.e. coefficient of x in eq(2))
and eq(2) by 3 (i.e. coefficient of x in eq(1))

and subtract.

Now, if we want to eliminate y from both the equations:

multiply eq(1) by 3 (i.e. coefficient of y in eq(2))
and eq(2) by 6 (i.e. coefficient of y in eq(1))

and subtract.

But here, in the (2) equation, we only need to multiply it with 2 so to get 6y in (2) equation because we need to eliminate y from both the equations.
Rest, others numbers like 4 ,5 , we can't take them here, as there is no need. Because we won't able to eliminate either x or y term from the given equations.

In other words,
In elimination method, we eliminate one of the variables from the given equations. So, we need to multiply the given equations with a suitable numbers so that we can add or subtract the given equations.
Hence, then only one of variable (either x or y) will be cancel out. Then to find out other value of second variable (either x or y) by substituting this value in one of the given equations.

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