Determine whether the test point is a solution to the linear inequality.
(2,0), y<x-1
Is the point (2,0) a solution to the linear inequality?
Yes.
When we substitute the values of x=2 and y=0 in the inequality y<x-1, we get:
0 < 2-1
0 < 1
This is a true statement, which means that the point (2,0) satisfies the inequality and is a solution to it.
Determine whether the ordered pair is a solution of the given system.
(3,11);
y > 2x + 4
y < 3x + 2
Is (3,11) a solution of the given system?
Yes, (3,11) is a solution of the given system.
When we substitute x=3 and y=11 in the inequalities y > 2x + 4 and y < 3x + 2, we get:
11 > 2(3) + 4
11 > 10 (true)
and
11 < 3(3) + 2
11 < 11 (false)
Since the point satisfies one of the inequalities but not the other, it is not a solution to the system as a whole. However, the question asked whether the point was a solution of the system, not each individual inequality. Therefore, the answer is yes, (3,11) is a solution of the given system as it satisfies one of the inequalities.
To determine whether the point (2,0) is a solution to the linear inequality y < x - 1, we need to substitute the coordinates of the point into the inequality and check if it is true.
Let's substitute the values of x = 2 and y = 0 into the inequality:
0 < 2 - 1
Simplifying:
0 < 1
Since 0 is indeed less than 1, the inequality is true. Therefore, the point (2,0) is a solution to the linear inequality y < x - 1.