Class 10 Exam > Class 10 Questions > Pair of linear equations x+2y+5 = 0 and 3x+6y...
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Pair of linear equations x+2y+5 = 0 and 3x+6y -1 = 0 have
- a)unique solution
- b)exactly two solutions
- c)infinitely many solutions
- d)no solution
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Pair of linear equations x+2y+5 = 0 and 3x+6y -1 = 0 havea)unique solu...
Given, .... x+2y+5 = 0 and 3x+6y-1= 0.....
Let a1 = 1, b1 =2, c1=5....a2=3, b2=6, c2= -1....
This pair of linear equation satisfies the formula : a1/a2 = b1/b2 ≠ c1/c2..... ie., 1/3= 1/3 ≠5/-1.....
And hence..... option D is the correct answer... because this equation has NO SOLUTION.....
Let a1 = 1, b1 =2, c1=5....a2=3, b2=6, c2= -1....
This pair of linear equation satisfies the formula : a1/a2 = b1/b2 ≠ c1/c2..... ie., 1/3= 1/3 ≠5/-1.....
And hence..... option D is the correct answer... because this equation has NO SOLUTION.....
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Community Answer
Pair of linear equations x+2y+5 = 0 and 3x+6y -1 = 0 havea)unique solu...
To determine the solution to the given system of equations, let's analyze each equation separately and then combine them to find the solution.
Equation 1: x + 2y - 5 = 0
Equation 2: 3x + 6y - 1 = 0
Solving Equation 1:
Rearrange equation 1 in terms of x:
x = 5 - 2y
Solving Equation 2:
Rearrange equation 2 in terms of x:
3x = 1 - 6y
x = (1 - 6y)/3
x = (1/3) - 2y
Comparing the Equations:
Now, we can compare the two expressions for x:
x = 5 - 2y
x = (1/3) - 2y
Both expressions are equal to x, so we can equate them:
5 - 2y = (1/3) - 2y
Conclusion:
From the above equation, we can see that the variable y cancels out. This results in a contradiction: 5 is not equal to 1/3.
Hence, the system of equations is inconsistent and has no solution. Therefore, the correct answer is option 'D' - no solution.
Equation 1: x + 2y - 5 = 0
Equation 2: 3x + 6y - 1 = 0
Solving Equation 1:
Rearrange equation 1 in terms of x:
x = 5 - 2y
Solving Equation 2:
Rearrange equation 2 in terms of x:
3x = 1 - 6y
x = (1 - 6y)/3
x = (1/3) - 2y
Comparing the Equations:
Now, we can compare the two expressions for x:
x = 5 - 2y
x = (1/3) - 2y
Both expressions are equal to x, so we can equate them:
5 - 2y = (1/3) - 2y
Conclusion:
From the above equation, we can see that the variable y cancels out. This results in a contradiction: 5 is not equal to 1/3.
Hence, the system of equations is inconsistent and has no solution. Therefore, the correct answer is option 'D' - no solution.
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Pair of linear equations x+2y+5 = 0 and 3x+6y -1 = 0 havea)unique solutionb)exactly two solutionsc)infinitely many solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer?
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