Question

Is the point (4,1) In the solution set for the following system of linear inequalities?

x>3
y2-2
x + y < 6

Answer 1

Yes, the point (4,1) is in the solution set for the system of linear inequalities.

For the inequality x > 3, since 4 is greater than 3, the point (4,1) satisfies this inequality.

For the inequality y < 2, since 1 is less than 2, the point (4,1) satisfies this inequality.

For the inequality x + y < 6, if we substitute x = 4 and y = 1, we get 4 + 1 < 6, which is true. Therefore, the point (4,1) also satisfies this inequality.

Since the point (4,1) satisfies all three inequalities, it is in the solution set for the system of linear inequalities.