Answer:
(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).
