Question

Which of the following points is a solution to the system of linear inequalities

Which of the following points is a solution to the system of linear inequalities?
{2x+y<-5
{-x+y>0
A.
(4, 1)
B.
(–4, –1)
C.
(–8, –21)
D.
(8, 11)

Answer 1

for it to be a solution, it has to satisfy both inequalities...

subbing in (-4,-1)

2x + y < -5 -x + y > 0
2(-4) - 1 < - 5 -(-4) - 1 > 0
-8 - 1 < -5 4 - 1 > 0
-9 < -5.....true 3 > 0....true

solution is (-4,-1)

Answer 2

(-4,-1) satisfies the given system of inequalities

Explanation:

`2x+y<-5`

`-x+y>0`

To find out the solution we check with each option

(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)

`2(4)+1<-5`

`9<-5` False

(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)

`2(-4)-1<-5`

`-9<-5` True

Now plug it in second inequality

`-(-4)-1>0`

`3>0` True

(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)

`2(-8)-21<-5`

`-37<-5` True

Now plug it in second inequality

`-(-8)-21>0`

`-13>0` False

(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)

`2(8)+11<-5`

`-9<-5` false