for the system of inequalities y >= 2x - 1 and y <= 3x - 1, which of the following statements best descibes the ordered pair (1,1)
a)The point (1,1) is a solution for y >= 2x - 1, but not y <= 3x - 1.
b) The point (1,1) is not a solution for either equation.
c)The point (1,1) is a solution for the entire system.
d)The point (1,1) is a solution for y <= 3x - 1, but not for y >= 2x - 1
d
To determine if the point (1,1) is a solution for the system of inequalities, let's substitute the x and y values of the point into each inequality and see if the inequalities are satisfied.
For the first inequality, y >= 2x - 1:
Substituting x = 1 and y = 1, we have 1 >= 2(1) - 1.
Simplifying, 1 >= 2 - 1.
This is true, as 1 >= 1.
For the second inequality, y <= 3x - 1:
Substituting x = 1 and y = 1, we have 1 <= 3(1) - 1.
Simplifying, 1 <= 3 - 1.
This is true, as 1 <= 2.
Since the point (1,1) satisfies both inequalities, it is a solution for the entire system.
Therefore, the correct answer is:
c) The point (1,1) is a solution for the entire system.
To determine if the ordered pair (1,1) is a solution for the system of inequalities y ≥ 2x - 1 and y ≤ 3x - 1, we substitute the values of x and y into both inequalities.
For the inequality y ≥ 2x - 1:
1 ≥ 2(1) - 1
1 ≥ 2 - 1
1 ≥ 1
The inequality is true, so the ordered pair (1,1) is a solution for y ≥ 2x - 1.
For the inequality y ≤ 3x - 1:
1 ≤ 3(1) - 1
1 ≤ 3 - 1
1 ≤ 2
The inequality is also true, so the ordered pair (1,1) is a solution for y ≤ 3x - 1.
Therefore, the correct statement is: The point (1,1) is a solution for the entire system. Therefore, the answer is c) The point (1,1) is a solution for the entire system.