41(x)+16(y)=1 find the value of x and y

There are infinite values for 'x' and 'y' if you have two variable and only ONE equation

to find a discrete (x,y) solution you will need two equations relating x and y.

41x + 16y = 1 

 

So normally if u have 2 unknown variables u should try to first focus on one variable. I will try to focus on y.

 

41x + 16y = 1        II -41x

 

By doing this im isolating the y on one side.

 

16y = 1 - 41x     II /16

 

y = (1/16)   -   (41x/16)

 

Now we got y. As u dont have either x or y given, this is the farthest u can go. U just have to input a number for x, and though can calculate the y value.

Little example:

U take the number x =1 

 

y = 1/16   -   41/16 

= (- 40/16) = -2.5

 

Which means 41 * 1 + 16 * (-2.5)   = 1 

what is correct.

 

Other way around:

41x + 16y = 1                 II -16y

41x           = 1 - 16y        II  /41

x               = (1/41) - (16y/41)

 

          

 

U would need 2 equations to solve 2 unknown variables. 

U need n equations to solve n unknown variables.  ( I think this is right, but not sure.)

The answer to ur question is that the values of x and y are always dependent from x or y. This can be shown in the following two forms:

(     x      /         (1/16) - (41x/16)     )

                      and

(    (1/41) - (16y/41)      /       y      )

 

and to show that in form of math:

if u put either x or y into ur starting equation u get a result like 1=1

41x + 16y = 1 

putting in the equation for x: (dont forget brackets, important)

 

41 * ( (1/41) - (16y/41) )  + 16y = 1

1 - 16y + 16y = 1

1 = 1

This shows there are infinite answers to the equation.