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The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –
- a)k = 2
- b)k = 6
- c)k = 6
- d)k = 3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many so...
An equation has infinitely many solutions when the lines are coincident.
The lines are coincident when
So 3x + 4y = k, 9x + 12y = 6 are coincident when
The lines are coincident when
So 3x + 4y = k, 9x + 12y = 6 are coincident when
Most Upvoted Answer
The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many so...
The two equations are multiples of each other.
To see why, let's write the first equation in terms of y:
3x - k/4 = y
Now substitute this expression for y into the second equation:
9x - 12(3x - k/4) = 6
Simplifying and solving for k, we get:
k = 24
So the pair of equations 3x - 4y = 24 and 9x - 12y = 6 are multiples of each other.
To find the infinitely many solutions, we can solve either equation for one variable in terms of the other and then substitute into the other equation. For example, solving the first equation for y, we get:
y = (3x - k/4)/4
Substituting this into the second equation, we get:
9x - 12(3x - k/4) = 6
Simplifying and solving for x, we get:
x = 2
Substituting this back into the equation for y, we get:
y = (3(2) - k/4)/4 = (6 - k/4)/4
So the solutions are given by the ordered pairs (2, (6 - k/4)/4) for all values of k.
To see why, let's write the first equation in terms of y:
3x - k/4 = y
Now substitute this expression for y into the second equation:
9x - 12(3x - k/4) = 6
Simplifying and solving for k, we get:
k = 24
So the pair of equations 3x - 4y = 24 and 9x - 12y = 6 are multiples of each other.
To find the infinitely many solutions, we can solve either equation for one variable in terms of the other and then substitute into the other equation. For example, solving the first equation for y, we get:
y = (3x - k/4)/4
Substituting this into the second equation, we get:
9x - 12(3x - k/4) = 6
Simplifying and solving for x, we get:
x = 2
Substituting this back into the equation for y, we get:
y = (3(2) - k/4)/4 = (6 - k/4)/4
So the solutions are given by the ordered pairs (2, (6 - k/4)/4) for all values of k.
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Community Answer
The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many so...
Option A
Since ratio is 1/3 and all ratio should be equal
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The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –a)k = 2b)k = 6c)k = 6d)k = 3Correct answer is option 'A'. Can you explain this answer?
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