Question

How can one fourthx − 3 = one halfx + 8 be set up as a system of equations?

Answer 1

The answer is B.

The reason being is that in this option they have set both sides of the equation separately equal to y. Since they are equal to each other, they would both have to be equal to an unknown y. This would look like this.
y = 1/4x - 3
y = 1/2x + 8.

Then to remove the fractions in each, they multiplied by the denominator associated with x. So, you multiply the first equation by 4.
4y = x - 12.
Then they solve for the numerical value at the end.
4y - x = -12.

You can do the same with the second equation.
y = 1/2x + 8
2y = x + 16
2y - x = 16

These are now the two equations above.