Fast! will mark as brainliest if given good answer!

which of the following points lie in the solution set the following system of inequalities? show your work to justify your answer
y < -3x + 3
y < x + 2

1. (1,-5)
2.(1,5)
3. (5,1)
4. (-1,5)

(1,-5) is a solution.

Step-by-step explanation:

The easiest way to do this is to plug in the choices and see which point satisfies both inequalities.

1. (1,-5)?

(x,y)=(1,-5)

y<-3x+3

-5<-3(1)+3

-5<-3+3

-5<0 is true

(x,y)=(1,-5)

-5<1+2

-5<3 is true

So (1,-5) is a point in the solution field.

2. (1,5)?

(x,y)=(1,5)

y<-3x+3

5<-3(1)+3

5<-3+3

5<0 is false.

We do not have to try the other inequality as this one already said it was not a solution.

It has to satisfy both inequalities (all the conditions).

(1,5) is not a solution.

3. (5,1)?

(x,y)=(5,1)

y<-3x+3

1<-3(5)+3

1<-15+3

1<-12 is false.

So (5,1) is not a solution.

4. (-1,5)?

(x,y)=(-1,5)

y<-3x+3

5<-3(-1)+3

5<3+3

5<6 is true.

(x,y)=(-1,5)

y<x+2

5<-1+2

5<1 is false.

So (-1,5) is not a solution.

------------I went ahead and graphed the system too.------------

y<-3x+3 says to shade below y=-3x+3.

y=-3x+3 has slope -3/1 and y-intercept 3.

So I graphed 3 on the y-axis first and then I used -3/1 to find the point (1,0) to graph y=-3x+3.

y<x+2 says to shade below y=x+2.

y=x+2 has slope 1/1 and y-intercept 2.

So I graphed 2 on the y-axis first then I used 1/1 to find the point (1,3) to graph y=x+2.

Please see visual now.

(1,-5) is the only one in the intersection of the coloring (both colorings).