Question

please help!
Which of the following points lie in the solution set to the following system of inequalities?y < −3x + 3y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)

Answer 1

Answer:

(1,-5)

Step-by-step explanation:

The given system of inequalities are;

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

and

$y\:<\:x+2$

The point that is a solution will satisfy the two inequalities.

Checking for (1,-5)

$-5\:<\:-3(1)+3$ and $-5\:<\:1+2$

$-5\:<\:0$: True $-5\:<\:3$ : True

This point lies in the solution region.

Checking for (1,5)

$5\:<\:-3(1)+3$ and $5\:<\:1+2$

$5\:<\:0$: False $5\:<\:3$ : False

This point does not lie in the solution region.

Checking for (5,1)

$1\:<\:-3(5)+3$ and $1\:<\:5+2$

$1\:<\:-12$: False $1\:<\:7$ : True

This point does not lie in the solution region.

Checking for (-1,5)

$5\:<\:-3(-1)+3$ and $5\:<\:-1+2$

$5\:<\:6$: True $5\:<\:1$ : False

This point does not lie in the solution region.

Answer 2

Plug the values and check if they return a true statement or not:

Plugging $(x,y) = (1,-5)$ we have

$-5 < -3 -15 < 1 + 2 \iff -5 < -18 < 3$ which is false

Plugging $(x,y) = (1,5)$ we have

$5 < -3 +15 < 1 + 2 \iff 5 < 12 < 3$ which is false

Plugging $(x,y) = (5, 1)$ we have

$1 < -15 + 3 < 5 + 2 \iff 1 < -12 < 7$ which is false

Plugging $(x,y) = (-1, 5)$ we have

$5 < 3 +15 < -1 + 2 \iff 5 < 18 < 1$ which is false

So, all of the options seem wrong.