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Find the number of non-negative integral points that satisfy 2x + y > 16 and x + 2y = 20.
- a)8
- b)9
- c)10
- d)11
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the number of non-negative integral points that satisfy 2x + y &g...
Number of non-negative integral points on x + 2y = 20 ⇒ (20,0), (18,1),......,(2,9) and (0,10) ⇒ 11 points
Intersection point of 2x + y = 16 and x + 2y = 20 is (4,8)
So, all the points among the above 11 points that have x coefficient less than or equal to 4 are removed.
⇒ 3 points are removed.
Hence, required number of points = 11 - 3 = 8
Intersection point of 2x + y = 16 and x + 2y = 20 is (4,8)
So, all the points among the above 11 points that have x coefficient less than or equal to 4 are removed.
⇒ 3 points are removed.
Hence, required number of points = 11 - 3 = 8
Most Upvoted Answer
Find the number of non-negative integral points that satisfy 2x + y &g...
We can start by graphing the inequality $2x+y<10$ on="" the="" coordinate="" plane.="">
To do this, we can first graph the line $2x+y=10$, which passes through the points $(0,10)$ and $(5,0)$. This line serves as the boundary between the points that satisfy the inequality and those that do not.
Next, we need to determine which side of the line satisfies the inequality. We can choose a test point, such as $(0,0)$, and substitute its coordinates into the inequality:
$2(0) + 0 < />
$0<10$>
Since this is true, we know that the region below the line satisfies the inequality.
Now we need to count the number of non-negative integral points within this region. We can start by counting the points along the $x$-axis and $y$-axis.
On the $x$-axis, we have the points $(0,0)$, $(1,0)$, $(2,0)$, $(3,0)$, $(4,0)$, and $(5,0)$.
On the $y$-axis, we have the points $(0,0)$, $(0,1)$, $(0,2)$, $(0,3)$, $(0,4)$, $(0,5)$, $(0,6)$, $(0,7)$, $(0,8)$, and $(0,9)$.
We can see that there are 11 points on the $x$-axis and 10 points on the $y$-axis. However, we need to be careful not to overcount the point $(0,0)$, which is on both axes.
Therefore, the total number of non-negative integral points that satisfy the inequality is $11+10-1=\boxed{20}$.
To do this, we can first graph the line $2x+y=10$, which passes through the points $(0,10)$ and $(5,0)$. This line serves as the boundary between the points that satisfy the inequality and those that do not.
Next, we need to determine which side of the line satisfies the inequality. We can choose a test point, such as $(0,0)$, and substitute its coordinates into the inequality:
$2(0) + 0 < />
$0<10$>
Since this is true, we know that the region below the line satisfies the inequality.
Now we need to count the number of non-negative integral points within this region. We can start by counting the points along the $x$-axis and $y$-axis.
On the $x$-axis, we have the points $(0,0)$, $(1,0)$, $(2,0)$, $(3,0)$, $(4,0)$, and $(5,0)$.
On the $y$-axis, we have the points $(0,0)$, $(0,1)$, $(0,2)$, $(0,3)$, $(0,4)$, $(0,5)$, $(0,6)$, $(0,7)$, $(0,8)$, and $(0,9)$.
We can see that there are 11 points on the $x$-axis and 10 points on the $y$-axis. However, we need to be careful not to overcount the point $(0,0)$, which is on both axes.
Therefore, the total number of non-negative integral points that satisfy the inequality is $11+10-1=\boxed{20}$.
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Find the number of non-negative integral points that satisfy 2x + y > 16 and x + 2y = 20.a)8b)9c)10d)11Correct answer is option 'A'. Can you explain this answer?
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