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Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?
- a)a ≠ -2
- b)a = -2
- c)a = 2
- d)a ≠ 2
Correct answer is option 'A'. Can you explain this answer?
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Find the value of ‘a” for which the system of equations ax...
The given equations are : ax + 2y – 4 = 0, x – y – 3 = 0
is a case of intersecting lines which meet at one.
Here a1=a,a2=1,b1=2,b2=-1
is a case of intersecting lines which meet at one.Here a1=a,a2=1,b1=2,b2=-1
Most Upvoted Answer
Find the value of ‘a” for which the system of equations ax...
To find the value of 'a' for which the given system of equations represents intersecting lines, we need to determine the condition under which the lines are not parallel.
Given system of equations:
1) ax + 2y - 4 = 0
2) x + y - 3 = 0
Let's solve these equations to find the values of 'x' and 'y' in terms of 'a':
1) ax + 2y - 4 = 0
2y = -ax + 4
y = (-ax + 4)/2
y = -ax/2 + 2
2) x + y - 3 = 0
x + (-ax/2 + 2) - 3 = 0
x - ax/2 - 1 = 0
x(1 - a/2) = 1
x = 1/(1 - a/2)
Now, we can see that the slopes of the lines are -a/2 and -1 respectively because the coefficient of 'x' represents the slope of the line. For the lines to intersect, their slopes should be different.
If the lines are parallel, their slopes are equal. So, let's set the slopes equal to each other and solve for 'a':
-a/2 = -1
a/2 = 1
a = 2
Therefore, the value of 'a' for which the given system of equations represents intersecting lines is a = 2.
Hence, the correct answer is option 'A' (a = -2).
Given system of equations:
1) ax + 2y - 4 = 0
2) x + y - 3 = 0
Let's solve these equations to find the values of 'x' and 'y' in terms of 'a':
1) ax + 2y - 4 = 0
2y = -ax + 4
y = (-ax + 4)/2
y = -ax/2 + 2
2) x + y - 3 = 0
x + (-ax/2 + 2) - 3 = 0
x - ax/2 - 1 = 0
x(1 - a/2) = 1
x = 1/(1 - a/2)
Now, we can see that the slopes of the lines are -a/2 and -1 respectively because the coefficient of 'x' represents the slope of the line. For the lines to intersect, their slopes should be different.
If the lines are parallel, their slopes are equal. So, let's set the slopes equal to each other and solve for 'a':
-a/2 = -1
a/2 = 1
a = 2
Therefore, the value of 'a' for which the given system of equations represents intersecting lines is a = 2.
Hence, the correct answer is option 'A' (a = -2).
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Find the value of ‘a” for which the system of equations ax...
A) one is the answer
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Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?a)a ≠ -2b)a = -2c)a = 2d)a ≠ 2Correct answer is option 'A'. Can you explain this answer?
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Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?a)a ≠ -2b)a = -2c)a = 2d)a ≠ 2Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?a)a ≠ -2b)a = -2c)a = 2d)a ≠ 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?a)a ≠ -2b)a = -2c)a = 2d)a ≠ 2Correct answer is option 'A'. Can you explain this answer?.
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