How can one sixthx − 5 = one fifthx + 2 be set up as a system of equations?

For problems like these, we can set both sides of the equation equal to y. This is because both sides of the equation are equal to each other. If we were to take the left side of the equation and set it equal to y, the right side would also be equal to y. Similarly, if we were to set the right side of the equation equal to y, the left side of the equation would also be equal to y. Setting both equations equal to y will produce two equations which can be used in a system of equations.

Thus, our answer is:
y = (1/6)x - 5
y = (1/5)x + 2