The system of equations above is satisfied by which of the following ordered pairs (x, y) ?
A) (–5, 4)
B) (4, –2)
C) (5, 4)
D) (5, –4)Which Way?
Sometimes, it’s hard to
tell if you need a larger
number or a smaller num-
ber if the first answer you
tried didn’t work. Don’t
fret. Just pick a direction
and go! Spend your time
trying answers rather than
worrying about going in
the wrong direction.Here’s How to Crack It
When you feel the urge to do a whole lot of algebra, it is a good time to check whether it would be
possible to just plug in the answers instead. In this case, trying your answer choices will be not only
effective but also incredibly fast.
It doesn’t seem like we will be able to tell whether to move up or down this time, as the ordered pairs
don’t really have an ascending or descending order, but let’s start in the middle anyway. Even if you end
up trying all four, you will be saving time by plugging in the answers instead of solving.
Starting with (B) gives you 4 for x and –2 for y. Try that out in the first equation: 2(4) + (–2) = 6. That
matches the first equation, so this is a possibility. Let’s try it out in the second equation: 7(4) + 2(–2) =
- That does not match the second equation, so you can eliminate (B).
Let’s try out (C) next. If x = 5 and y = 4, then 2(5) + 4 = 14, and you wanted it to be 6, so you can
eliminate this answer choice, too.
Let’s move on to (D). That would give you 2(5) + (–4) = 6. So far so good! Let’s try the second equation
to see if this choice satisfies both: 7(5) + 2(–4) = 27. Since (D) satisfies both equations, this is your
answer!
You may recall that we covered questions like this in the last chapter. It is important to know how to solve
these, in case a question like this comes up in the Grid-In part of a Math section. When you have answers
available to you, though, don’t be afraid to use them!