Class 10 Exam > Class 10 Questions > The pairs of equations 9x + 3y + 12 = 0 and 1...
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The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
- a)Unique solution
- b)Exactly two solutions
- c)No solution
- d)Infinitely many solutions
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)Un...
Given, 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0
a1/a2 = 9/18 = 1/2
b1/b2 = 3/6 = 1/2
c1/c2 = 12/26 = 6/13
Since, a1/a2 = b1/b2 ≠ c1/c2
So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.
a1/a2 = 9/18 = 1/2
b1/b2 = 3/6 = 1/2
c1/c2 = 12/26 = 6/13
Since, a1/a2 = b1/b2 ≠ c1/c2
So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.
Most Upvoted Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)Un...
Given equations are 9x - 3y + 12 = 0 and 18x - 6y + 26 = 0.
To find the solution, we can simplify the equations by dividing both sides of each equation by 3. This gives us:
3x - y + 4 = 0 and 6x - 2y + 13/3 = 0
Now, we can use the method of elimination to solve for x and y. Multiplying the first equation by 2 and subtracting it from the second equation, we get:
(6x - 2y + 13/3) - 2(3x - y + 4) = 0
Simplifying this, we get:
-4y + 5/3 = 0
Solving for y, we get:
y = 5/12
Substituting this value of y in the first equation, we get:
3x - 5/12 + 4 = 0
Solving for x, we get:
x = -47/108
Therefore, the system of equations has no solution as x and y do not satisfy both equations simultaneously.
Hence, the correct answer is option C, i.e., "No solution."
To find the solution, we can simplify the equations by dividing both sides of each equation by 3. This gives us:
3x - y + 4 = 0 and 6x - 2y + 13/3 = 0
Now, we can use the method of elimination to solve for x and y. Multiplying the first equation by 2 and subtracting it from the second equation, we get:
(6x - 2y + 13/3) - 2(3x - y + 4) = 0
Simplifying this, we get:
-4y + 5/3 = 0
Solving for y, we get:
y = 5/12
Substituting this value of y in the first equation, we get:
3x - 5/12 + 4 = 0
Solving for x, we get:
x = -47/108
Therefore, the system of equations has no solution as x and y do not satisfy both equations simultaneously.
Hence, the correct answer is option C, i.e., "No solution."
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Community Answer
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 havea)Un...
A = 9 , b = 3 and c= 12
A = 18 , B = 6 and C = 26
let us consider the property of No solution
a/A = b/B ≠ c/ C
9/ 18 = 3/6 ≠ 12/26
1/2=1/2≠12/26
hence, the given equation have no solution.
option C. is correct
A = 18 , B = 6 and C = 26
let us consider the property of No solution
a/A = b/B ≠ c/ C
9/ 18 = 3/6 ≠ 12/26
1/2=1/2≠12/26
hence, the given equation have no solution.
option C. is correct
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