"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0\le x, y The graph of$$3x\equiv 4y-1 \pmod{35}$$has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<35$.

What is the value of $x_0+y_0$?

is the number L such that

Consider the first 7 multiples of 5:

5, 10, 15, 20, 25, 30, 35

Taken mod 7, these are equivalent to

5, 3, 1, 6, 4, 2, 0

This tells us that 3 is the inverse of 5 mod 7, so L = 3.

Similarly, compute the inverses modulo 7 of 2 and 3:

since 2*4 = 8, whose residue is 1 mod 7;

which we got for free by finding the inverse of 5 earlier. So

and so R = 2.

Then L - R = 1.

c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )