SOLUTION: x+y>3 ax+2y<-2 In the system of inequalities, a is a constant. If the system has no solution, What is the value of a? A) -2 B) -1 C) 1 D) 2

Question 1043524: x+y>3
ax+2y<-2
In the system of inequalities, a is a constant. If the system has no solution, What is the value of a?
A) -2
B) -1
C) 1
D) 2
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
x�y=3 and ax+2y=-2 are linear equations,
so they graph as straight lines,
If the lines do not have the same slope,
They are not parallel, and
they will intersect forming 4 angles.
Then, one of those angles will ve the solution.
If there is no solution,
the lines must be parallel (same slope).
The slope of x+y=3 <---> y=-�+3 is -1.
The slope of ax+2y=-2 <---> 2y=-ax-2 <---> y=(-a/2)x-1 is -a/2.
So, for the lines to be parallel,
It must be 'a/2=-1 ---> a=2
When a=2, the second inequality is
2x+2y=-2 <---> x+y<-1,
which cannot happen if x+y>3.
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