Is the point (4,1) In the solution set for the following system of linear inequalities?
x>3
y2-2
x + y < 6
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.
To determine if the point (4,1) is in the solution set for the system of linear inequalities, we need to substitute the values of x and y into each inequality and see if they are all true. Let's go step-by-step.
1. x > 3:
Is 4 greater than 3? Yes, it is. So, the first inequality is true.
2. y < 2:
Is 1 less than 2? Yes, it is. So, the second inequality is also true.
3. x + y < 6:
Is 4 + 1 less than 6? Yes, it is. So, the third inequality is true.
Since all three inequalities are true when we substitute the values of x = 4 and y = 1 into them, the point (4,1) is in the solution set for the given system of linear inequalities.