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.