Question

Please help me with these questions, I'm really struggling.

Which of the following ordered pairs is included in the solution set of the system, y < 2 - 2x and y > 2x -3?
Answers:
(0, 0)
(3, 4)
(4, 0)
No Solution


Choose all correct answers. Which of the following are solutions of the system?
x < 3 and x + y < 5
Answers:
4,2
2,2
-1,0
2,-1




Which one of the following is a solution of the system?
y <-1 and y > 8
6,9
-2,4
0,0
No solution

Answer 1

You just plug in the value for x and y for the first problem using the (x,y) values given as possible solutions.

So the first problem y< 2-2x and y> 2x-3. Start with first possible solution (0,0). So plug in x=0 and y=0 into both inequalities.

0< 2-(2)(0) Which gives us 0<2 which is true.

Now the other one 0>(2)(0)-3 Which gives us 0>-3 which is also true.

Since (0,0) is true for both inequalities, then (0,0) is a solution.

Let's check another possible solution (3,4). So we plug in x=3 and y=4 into both inequalities.

4<2-(2)(3) Which gives us 4<-4 which is false.

Now check the other one.
4>(2)(3)-3 Which gives us 4>3 which is also false.

Since (3,4) is false for at least one inequality, then it is not a solution.

You do the same process for the other possible solution.


For the other two questions, use the same process. However, some of the inequalities are not using both variables (x,y). So just plug in the one you need.

For example x<3, you only need the x value of the (x,y) values. So the first possible solution is (4,2). So only use the x=4 value.

You will have 4<3 which is false. The minute you get a false for either inequality, that possible solution is not a solution, and you can move on to the next possible solution.