Class 10 Exam > Class 10 Questions > The pair of linear equations 3x + 7y = k, 12x...
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The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not have any solution if
- a)k = 7
- b)k = 14
- c)k = 21
- d)k = 28
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not ha...
3/12 = 7/2k [ applying a1/a2=b1/b2 ]
3 x 2k = 7 x 12
k=14
3 x 2k = 7 x 12
k=14
Most Upvoted Answer
The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not ha...
Explanation:
Given pair of linear equations are:
3x - 7y = k ...(1)
12x - 2ky = 4k - 1 ...(2)
We need to find the value of k for which these equations do not have any solution.
Method:
If a pair of linear equations do not have any solution, it means they are inconsistent. Two linear equations are inconsistent if their slopes are equal but their y-intercepts are not equal.
We can rearrange the given equations into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Equation (1) can be rearranged as:
y = (3/7)x - (k/7) ...(3)
Equation (2) can be rearranged as:
y = (6/k)x - (2k-1)/(2k) ...(4)
Comparing equations (3) and (4), we get:
m1 = 3/7 and m2 = 6/k
For the pair of equations to be inconsistent, m1 = m2 and b1 ≠ b2.
Equating the slopes, we get:
3/7 = 6/k
Solving for k, we get:
k = 14
Now, substituting k = 14 in equations (1) and (2), we get:
3x - 7y = 14 ...(5)
12x - 28y = 55 ...(6)
Multiplying equation (5) by 4, we get:
12x - 28y = 56 ...(7)
Comparing equations (6) and (7), we see that the y-intercepts are not equal. Hence, the given pair of equations are consistent for k = 14.
Conclusion:
Thus, the given pair of linear equations 3x - 7y = k, 12x - 2ky = 4k - 1 do not have any solution if k = 14. Therefore, the correct option is (B).
Given pair of linear equations are:
3x - 7y = k ...(1)
12x - 2ky = 4k - 1 ...(2)
We need to find the value of k for which these equations do not have any solution.
Method:
If a pair of linear equations do not have any solution, it means they are inconsistent. Two linear equations are inconsistent if their slopes are equal but their y-intercepts are not equal.
We can rearrange the given equations into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Equation (1) can be rearranged as:
y = (3/7)x - (k/7) ...(3)
Equation (2) can be rearranged as:
y = (6/k)x - (2k-1)/(2k) ...(4)
Comparing equations (3) and (4), we get:
m1 = 3/7 and m2 = 6/k
For the pair of equations to be inconsistent, m1 = m2 and b1 ≠ b2.
Equating the slopes, we get:
3/7 = 6/k
Solving for k, we get:
k = 14
Now, substituting k = 14 in equations (1) and (2), we get:
3x - 7y = 14 ...(5)
12x - 28y = 55 ...(6)
Multiplying equation (5) by 4, we get:
12x - 28y = 56 ...(7)
Comparing equations (6) and (7), we see that the y-intercepts are not equal. Hence, the given pair of equations are consistent for k = 14.
Conclusion:
Thus, the given pair of linear equations 3x - 7y = k, 12x - 2ky = 4k - 1 do not have any solution if k = 14. Therefore, the correct option is (B).
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Community Answer
The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not ha...
Since the pair of linear equations do not have any solution , so,
a1/a2=b1/b2≠c1/c2
=>a1/a2=b1/b2
=>3/12=7/2k
=>1/4=7/2k
=>2k=4×7. ( cross-multiplication)
=>2k=28
=>k=14
a1/a2=b1/b2≠c1/c2
=>a1/a2=b1/b2
=>3/12=7/2k
=>1/4=7/2k
=>2k=4×7. ( cross-multiplication)
=>2k=28
=>k=14
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