Pleaseeeeeeeeeeee help

Question

x + y < -1

-3x + 2y <= 6

Check all that apply as solutions:

(5,7)

(-1,3)

(-4,-5)

(1,-2)

(6,-1)

Answer 1

You are looking for a solution for x and y that will make both statements true. Lets start with the first statement:

x+y<-1

now plug in each solution set to see if it works. We know that if x+y<-1, either. or y (or possibly both) will have to be negative. So (5,7) is not a solution for this inequality (5+7 is not less than -1).

if you plug in the other possible solutions we have:

-1 + 3 < -1 which simplifies to 2 < -1

-4 + (-5) < -1which simplifies to -9 < -1

1 + (-2) < -1which simplifies to -1 < -1

6 + (-1) < -1which simplifies to 5 < -1

Of these statements only the second one with the solution (-4,-5) is true.

Now we need to make sure that this solution satisfies the second equation. -3x + 2y <= 6

if you plug in (-4,-5) we get

-3*(-4) + 2*(-5)<=6

12+(-10)<= 6

2<= 6

So the solution (-4,-5) is the only solution that applies.

I hope this helped!