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.?
3x + 6y = 7000 .....(1)
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))
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))
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.
In elimination method, any one term of the same variable of one equation needs to be equal to one term of same variable of the second equation so as to eliminate them. Here they are multiplying by 2 in order to make the second term[3y] of the second equation equal to the second term[6y] of the first equation so as to eliminate them while subtracting both equations. We can use any number to multiply which will make the terms of the same variable equal.