SOLUTION: Hi ax-y=5 x+y=4 Answer is a>5/4. Need to find "a" values that make x and y positive. Explanations are greatly appreciated!! Thanks

Question 732550: Hi
ax-y=5
x+y=4
Answer is a>5/4. Need to find "a" values that make x and y positive. Explanations are greatly appreciated!!
Thanks
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Solve the system for x and y and get
x=9/(a+1) and y=(4a-5)/(a+1).

Note that .

Checking the result of y, Either numerator and denominator both positive OR numerator and denominator both negative.

I did not yet finish complete analysis but:
4a-5>0 AND a+1>0 means, through use of number line graphing, a>5/4
OR
4a-5<0 AND a+1<0 means, again through care with a number line, a<-1.

As said, not yet finished.

Checking how "a" works for x, we must have the denominator, a+1 POSITIVE so we say, ,
.
How does this fit with what was found for y? The part before the "OR" is what is consistant (tentatively) for . The part after the "OR" is no good in this problem description. Why? because MUST .

Now as long as we must have the conditions, and/or , the common set in these two is ;
So the answer is .
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