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

Answer:

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

Step-by-step 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