Hi Taylor,

Here's a different solution. Adding the two equations yields:

0 + 0 + c = 50

So, c = 50. Plugging this value for c back into the two given equations yields

a + b + 50/2 = 60
–a – b + 50/2 = –10

Simplifying the two equations yields

a + b = 35
–a – b = –35

Notice that the bottom equation can be obtained by merely multiplying the top equation by –1. So, we don't actually have a system of two equations here: we have just equation, a + b = 35, written two different ways. Since we have only one equation but two unknowns (a and b), there is not enough information to determine the value of b (or a). In general, you need as many unique equations as unknowns to determine the values of the unknowns, unless there is something special about the equations. But there is nothing special* here. We merely need two numbers that add up to 35. There are an infinite number of values of a and b for which this is true. For example, if a = 0 and b = 35, or a = 1 and b = 34.

* What do we mean by 'special.' Well, maybe for this system, we know that a is positive, though this would not be enough to determine the value of b. Or maybe we have a more complex equation, such as

a^2 + b^2 = 0

Here, we can determine the unique value of b. Both b and a must be zero:

0^2 + 0^2 = 0 + 0 = 0

Nova Press