Solve the Equation and find the value of X and Y?

I think you wanted to know the solution of this problem: A person gone to bank to draw a cheque. The amount written in cheque is X Rupees and Y Paise. He given the cheque to Bank Manager. But Bank manager mistakenly given Y Rupees and X Paise. By taking that amount he came out of bank and he buy a sweet with 20 Paise. After that he counted the amount. Then the amount is double than the cheque amount.

I have provided a method to guess the answer, as the calculation is very difficult and time consuming.

Coming to this question, you need two equations to solve two unknown variables. If there is only one equation with two variables, then there may be infinity number of solutions. However, with the given conditions that value x and y are integers, and x and Y are less than 100, there may be zero or one or few solutions. In this case, you need to try as follows: Substitute x= 1, find y using the equation y = (199 x +20) / 98. Y will not be a whole number. Then try x=2 and so on. You may use an excel sheet to generate the solution set. You have only one set of solution where x and y are whole numbers (26 and 53).

This could be rearranged as Y /(10/49) -- X / (20/199) = 1

So this will be straight line with positive slope and cutting the X axis at {(--20/199) ,0} and Y axis at {0, 10/49}. Thus there will be innumerable points on the line and hence the solution set will have infinite elements in it. For every possible value of x, you will definitely get one y.

The same situation would arise even when we come across two equations such as

x -- 2y = 7 and 3x -- 6y = 21.

It is only apparent. Actually there is only one statement. The second is nothing but got by multiplying throughout by 3.

resolve the equation for y might probable propose making y the undertaking of the equation, or in different words, changing our equation to "y = ..." So we try this: 4y = 9 - 15x y = (9 - 15x) / 4 Now substituting into this equation, the given value of x: y = [ 9 - 15 (-3) ] / 4 y = [ 9 + 40 5 ] / 4 y = fifty 4 / 4 y = 13.5

98y-199x-20=0=>

y=199x/98+20/98=>

y=2x+(3x+20)/98=>

take x=26, then

y=52+1=53

so, x=26, y=53 is a solution.

98Y-199X-20=0

98Y-199X=20

98Y=20+199X

98Y/98=20/98+199X/98

Y=20/98+199X/98

[Y=10/49+199X/98] <--this is the value of Y

98Y-199X=20

98Y-20=199X

98Y/199 - 20/199 = 199X/199

98Y/199 - 20/199 = X <--this is the value of X

The equation is a first order equation in two variables and we know that any first order equation represents a straight line with many set of values satisfying the equation. To get the value of x and y, just assume any value for x and get the value of y.

98Y - 199X - 20 = 0

98Y - 199X = 20

There seems to be no solution for this equation.

Y = (199X + 20)/98

X = (98Y - 20)/199

that is all you can do with that information

cannot give a single answer as there are 2 variable and only one statement

98Y - 199x = 20

so for y = 1

98 - 199x = 20, or 199x = 78, x = .392

for y = 2

196 - 199x = 20 or 176 = 199x, x = .884

etc etc

put y as any value to get corresponding value of x

ex:- when y =1 x = 78/199