Question

Which point is nor in the solution set of y<7x+6 and y<-7x+6 ?

a. (1,-2)
b. (0,5)
c. (2,15)
d. (2,-20)

Answer 1

The point that is not in the solution set of y < 7x + 6 and y < -7x + 6 is point C (2, 15).

Step-by-step explanation:

To find the point that is not in the solution set of the system of inequalities y < 7x+6 and y < -7x+6, we need to substitute the coordinates of each point into the inequalities and see if the statements hold.

Let's start with point A (1, -2).

Substituting the coordinates into the inequalities, we get:

• -2 < 7(1) + 6 --> -2 < 13
• -2 < -7(1) + 6 --> -2 < -1

Since both statements are true, point A satisfies both inequalities. Therefore, point A is in the solution set. Now, we can repeat this process with points B, C, and D to determine which point is not in the solution set.

Substituting the coordinates of point B (0, 5):

• 5 < 7(0) + 6 --> 5 < 6
• 5 < -7(0) + 6 --> 5 < 6

Since both statements are true, point B satisfies both inequalities. Now, let's move on to point C (2, 15):

• 15 < 7(2) + 6 --> 15 < 20
• 15 < -7(2) + 6 --> 15 < -8

Since the second statement is false, point C is not in the solution set. Finally, let's check point D (2, -20):

• -20 < 7(2) + 6 --> -20 < 20
• -20 < -7(2) + 6 --> -20 < -8

Again, the second statement is false, so point D is not in the solution set.

In conclusion, the point that is not in the solution set of y < 7x+6 and y < -7x+6 is point C (2, 15).