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
Did you test the point ???
for (1,1)
first equation: 1 ≥ 2-1 , or 1 ≥ 1, true
2nd equation: 1 ≤ 3-1 , or 1 ≤ 2, true
mmmhhh?
To determine whether the point (1,1) is a solution for the system of inequalities y >= 2x - 1 and y <= 3x - 1, we can substitute the values of x and y into each inequality and see if the statements hold true.
For the inequality y >= 2x - 1:
Substituting x = 1 and y = 1, we have:
1 >= 2(1) - 1
1 >= 1
The inequality is true, as 1 is indeed greater than or equal to 1.
For the inequality y <= 3x - 1:
Substituting x = 1 and y = 1, we have:
1 <= 3(1) - 1
1 <= 2
The inequality is true, as 1 is indeed less than or equal to 2.
Therefore, the point (1,1) satisfies both inequalities, making it a solution for the entire system of inequalities.
Hence, the correct answer is:
c) The point (1,1) is a solution for the entire system.