Question

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

Answer 1

Answer: (1, −5)

Step-by-step explanation:

Plot the given inequalities on coordinate plane.

For y < −3x + 3, plot y =−3x + 3

At x=0,  y= 3

At y =0, 0=-3x+3

⇒ x= 1

so, plot points (0,3) and (1,0) and join to get y =−3x + 3, since inequality has '<' sign, so shade( in red) below line area and line should be dotted.

For  y < x + 2, plot  y = x + 2

At x=0,  y= 2

At y =0, x=-2

so, plot points (0,2) and (-2,0) and join to get y = x + 2, since inequality has '<' sign, so shade( in orange) below line area and line should be dotted.

Now, plot all given points (1, −5) (1, 5) (5, 1) (−1, 5), we can clearly observe that (1, −5) lies in the solution set.  (in common shaded region)