must be an integer

In order to solve this, we need another equation! There are two unknowns, so we need two equations in order to find a solution. This is called solving a system of equations.

As you have it, this equation is a line. It can be rearranged into the slope-intercept form, y = mx + b:

4x + 3y = 149

*-4x -4x*

3y = -4x + 149

*3 3*

y = (-4/3)x + 149/3

If you had another equation which could also be put into y = mx + b form, then solving the system of equations would give you the coordinates for the intersection between the lines.

- If there was no solution, this would mean that the two lines were parallel and never crossed.
- If there were infinite solutions, this would mean that the two lines were in fact the same line, and therefore "crossed" at every point.

If all you really wanted were some integer solutions to that equation, here are some options:

(5, 43)

(8, 39)

(11, 35)

(14, 31)

(17, 27)