The point which will lie in the solution set to the following system of inequalities is:
(2,5)
The system of inequality is given by:
y>-3x+3--------(1)
and y>x+2----------(2)
Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.
a)
(2,-5)
when x=2 and y= -5
then by first inequality we have:
-5>-3×2+3
i.e.
-5>-6+3
i.e.
-5>-3
which is a false identity.
This means that the point will not lie in the solution set.
b)
(-2,5)
when x= -2 and y=5
then by first inequality we have:
5>-3×(-2)+3
i.e.
5>6+3
i.e.
5>9
which is a false identity.
Hence, option: b is incorrect.
c)
(2,5)
when x=2 and y=5
then by first inequality:
5>-3×2+3
i.e. 5>-6+3
i.e. 5>-3
which is true
and by second identity:
5>2+2
i.e. 5>4
which is again true.
Hence, (2,5) lie in the solution set.
d)
(-2,-5)
when x= -2 and y= -5
then by first inequality we have:
-5>-3×(-2)+3
i.e.
-5>6+3
i.e.
-5>9
which is a false identity.
Hence, the point (-2,-5) do not lie in the solution set.
