lunarpower wrote:<annoying administrative comment>
just fyi, you could easily type this problem into the forum directly, in something like 10-20% of the time it would take to take a screen shot and upload it to the forum.
and that would be easier for everyone.
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</annoying administrative comment>
step 1
REPHRASE THE QUESTION
xy > 0 means that x and y have the same sign.
so, the question can be rephrased as
do x and y have the same sign?
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step 2
INDIVIDUAL STATEMENTS
these are 2 linear inequalities; ALL linear inequalities include at least two neighboring quadrants of the xy-plane.
if you have two neighboring quadrants, then the signs of x and y are going to be the same in one of those quadrants, and opposite in the other one. (this is actually a very useful general takeaway; remember it)
therefore, each of the individual statements is insufficient.
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step 3
TWO STATEMENTS TOGETHER
here's the best, and simplest, rule to follow as far as combining inequalities:
you can add two inequalities if the inequality signs face the same way.
don't worry about subtracting inequalities - the rules are confusing and annoying. if you're in a situation where the inequalities where one is "<" and the other one is ">", and/or you want to subtract them in order to cancel something, just multiply by -1 and add them.
in these two inequalities,
both contain 'x', and the inequality signs are opposite. either one of these things
alone is a good enough reason to multiply by -1 and add, but, together, the case is overwhelmingly persuasive.
multiply inequality (2) by -1, giving
x - y > -2
2y - x > 6
add them:
y > 4
so, y is positive.
plug back into the first one:
x - 4 > -2
x > 2
so, x is also positive.
so, x and y have the same sign.
sufficient.
answer = c
