1/2 x = a

x + y = 5a

In the system of equations above, a is a constant such that 0 <a <1/3. If (x,y) is a solution to the system of equations, what is one possible value of y?

(Answer: 0 < x < 1)

The easiest way to go here is to plug in! Let’s say *a* = 0.1, which is certainly between 0 and 1/3.

The first equation tells us:

From there, we can solve for *y* in the second equation:

So there you go—grid in 0.3 as a possible value of *y* and move along.

To see the whole range of possible answers, plug in the endpoints you’re given for *a*.

If *a* = 0, then the first equation tells us that *x* = 0, too.

If *x* and *a* both equal zero, then the second equation becomes 0 + *y* = 5(0), which of course means *y* = 0, too!

OK, now plug in 1/3 for *a*. The first equation tells us:

Easy enough to solve for *y* in the second equation:

So if *a* = 0, *y* = 0, and if *a* = 1/3, *y* = 1. That’s why the full range of possible answers is 0 < *y* < 1.