Question
Th graph shows two lines representing the equations y = 2x + 5 and x + y = 1.
Which ordered pair is in the solution set for the system of inequalities y > 2x + 5 and x + y < 1?
( both of these (>,<) have a line underneath them )
A.) (-5,0)
B.) (0,7)
C.) (5,0)
D.) (0,-7)
Which ordered pair is in the solution set for the system of inequalities y > 2x + 5 and x + y < 1?
( both of these (>,<) have a line underneath them )
A.) (-5,0)
B.) (0,7)
C.) (5,0)
D.) (0,-7)
Answers
There are no human answers yet.
Answered by
GPT 3.5
To solve this system of inequalities, we need to find the ordered pairs that satisfy both inequalities.
For the inequality y > 2x + 5, we can start by finding points above the line y = 2x + 5. This means that values for y are greater than 2x + 5.
For the inequality x + y < 1, we need to find points below the line x + y = 1. This means the values for x and y are less than 1 when added together.
We can plot both lines on a graph and then determine which ordered pairs satisfy both inequalities:
The line y = 2x + 5 has a y-intercept of (0,5) and a slope of 2. Plotting this line, we see that it goes upwards from left to right.
The line x + y = 1 can be rearranged to y = -x + 1. It has a y-intercept of (0,1) and a slope of -1. This line goes downward from left to right.
Now, we need to look for points that are above the line y = 2x + 5 and below the line y = -x + 1.
Looking at the given options:
A.) (-5,0): This point is below the line y = 2x + 5 and above the line y = -x + 1. Thus, it does not satisfy both inequalities.
B.) (0,7): This point is above both lines, satisfying both inequalities.
C.) (5,0): This point is below both lines, not satisfying both inequalities.
D.) (0,-7): This point is below both lines, not satisfying both inequalities.
Therefore, the ordered pair in the solution set for the system of inequalities y > 2x + 5 and x + y < 1 is B.) (0,7).
For the inequality y > 2x + 5, we can start by finding points above the line y = 2x + 5. This means that values for y are greater than 2x + 5.
For the inequality x + y < 1, we need to find points below the line x + y = 1. This means the values for x and y are less than 1 when added together.
We can plot both lines on a graph and then determine which ordered pairs satisfy both inequalities:
The line y = 2x + 5 has a y-intercept of (0,5) and a slope of 2. Plotting this line, we see that it goes upwards from left to right.
The line x + y = 1 can be rearranged to y = -x + 1. It has a y-intercept of (0,1) and a slope of -1. This line goes downward from left to right.
Now, we need to look for points that are above the line y = 2x + 5 and below the line y = -x + 1.
Looking at the given options:
A.) (-5,0): This point is below the line y = 2x + 5 and above the line y = -x + 1. Thus, it does not satisfy both inequalities.
B.) (0,7): This point is above both lines, satisfying both inequalities.
C.) (5,0): This point is below both lines, not satisfying both inequalities.
D.) (0,-7): This point is below both lines, not satisfying both inequalities.
Therefore, the ordered pair in the solution set for the system of inequalities y > 2x + 5 and x + y < 1 is B.) (0,7).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.