Question
y ≤3x +1
x – y >1
Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?
- (−2, −1 )
- (−1, 3)
- (1, 5)
- (2, −1)
Hint:
Hint:- Inequalities are the mathematical expressions in which both sides are not
equal. In inequality, unlike in equations, we compare two values. The equal sign
in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to),
or not equal to sign.
There are two methods by which we can solve this question.
The correct answer is: (2, −1)
Solution:- Option D is correct.
Method 1:-
We have given two inequalities
y ≤3x +1
x – y >1
Any point (x, y) that is a solution to the given system of inequalities must
satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x − 1, the system is equivalent to the following system.
y ≤3x +1
x – y >1
Since , 3x + 1 > x − 1 for x > −1
and 3x + 1 ≤ x − 1 for x ≤ −1,
it follows that y < x − 1 for x > −1 and y ≤ 3x + 1 for x ≤ −1. Of the given choices,
only (2, −1) satisfies these conditions because −1 < 2 − 1 = 1
Method 2:-
Substituting (2, −1) into the first inequality gives
−1 ≤ 3(2) + 1, or −1 ≤ 7,
which is a true statement.
Substituting (2, −1) into the second inequality gives
2 − (−1) > 1, or 3 > 1,
which is a true statement.
Therefore, since (2, −1) satisfies both inequalities,
it is a solution to the system.
- If we considered Option A , it is incorrect because substituting −2 for x and −1
for y in the first inequality gives −1 ≤ 3(−2) + 1, or −1 ≤ −5, which is false.
- If we considered option B , it is incorrect because substituting −1 for x and 3 for
y in the first inequality gives 3 ≤ 3(−1) + 1, or 3 ≤ −2, which is false.
- If we considered option C, it is incorrect because substituting 1 for x and 5 for
y in the first inequality gives 5 ≤ 3(1) + 1, or 5 ≤ 4, which is false.
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So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
![](data:image/png;base64,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)
Point P is the center of the circle in the figure above. What is the value of x ?
![](data:image/png;base64,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)
Point P is the center of the circle in the figure above. What is the value of x ?
![](data:image/png;base64,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)
The circle above with center O has a circumference of 36. What is the length of minor arc
?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
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)
The circle above with center O has a circumference of 36. What is the length of minor arc
?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).