Question

Question 1 (1 point)
(05.06)
Which of the following points lie in the solution set to the following system of inequalities? (1 point)

y < −3x + 3
y < x + 2

a
(1, −5)

b
(1, 5)

c
(5, 1)

d
(−1, 5)

HELP PLEASE

Answer 1

Answer:

The points that lie in the solution set of following system of inequalities are:

Option A (1,-5) and Option C (5,1)

Step-by-step explanation:

We need to find the points that lie in the solution set to the following system of inequalities

$y<-3x+3\\y<x+2$

We will check each option to identify if they satisfy the given set of inequalities or net.

Option A (1,-5)

We have x=1, y=-5

Putting values and checking

$\\y<-3x+3\\-5<-3(1)+3\\-5<0 \ (true)\\y<x+2\\-5<1+2\\-5<3 \ (true)$

So, Option A is correct as both values satisfy the given set of equations

Option B (1,5)

We have x=1, y=5

Putting values and checking

$y<-3x+3\\5<-3(1)+3\\5<0 \ (false)\\y<x+2\\5<1+2\\5<3 \ (false)$

So, Option B is not correct as both values doesn't satisfy the given set of equations

Option C (5,1)

We have x=5, y=1

Putting values and checking

$y<-3x+3\\1<-3(5)+3\\1<-15+3\\1<12 \ (true)\\y<x+2\\1<5+2\\1<7 \ (true)$

So, Option C is correct as both values satisfy the given set of equations

Option D (-1,5)

We have x=-1, y=5

putting values and checking

$y<-3x+3\\5<-3(-1)+2\\5<3+2\\5<5 \ (false)\\y<x+2\\5<-1+2\\5<-1 \ (false)$

So, Option D is not correct as both values doesn't satisfy the given set of equations

The points that lie in the solution set of following system of inequalities are:

Option A (1,-5) and Option C (5,1)