Class 10 Exam > Class 10 Questions > The pair of equations x + 2y – 5 = 0 and −3x...
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The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:
- a)A unique solution
- b)Exactly two solutions
- c)Infinitely many solutions
- d)No solution
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:a)A u...
Here,
Here,
a1 / a2 = 1 / -3
b1 / b2 = 2 / -6 = 1 / -3
c1 / c2 = -5 / 15 = -1 / 3
This implies
a1 / a2 = b1 / b2 = c1 / c2
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The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:a)A u...
Solution:
The given pair of equations are:
x – 2y = 5 ...(i)
3x + 6y = 15 ...(ii)
On solving equations (i) and (ii), we get:
x = 2y + 5 ...(iii)
Substituting equation (iii) in equation (ii), we get:
3(2y + 5) + 6y = 15
⇒ 6y + 15 + 6y = 15
⇒ 12y = 0
⇒ y = 0
Substituting the value of y in equation (iii), we get:
x = 2(0) + 5
⇒ x = 5
Therefore, the solution of the given pair of equations is (5, 0).
Since we have obtained a unique solution for the given pair of equations, the correct option is (A).
However, the given answer is (C), which is incorrect. It seems like there is an error in the answer key.
The given pair of equations are:
x – 2y = 5 ...(i)
3x + 6y = 15 ...(ii)
On solving equations (i) and (ii), we get:
x = 2y + 5 ...(iii)
Substituting equation (iii) in equation (ii), we get:
3(2y + 5) + 6y = 15
⇒ 6y + 15 + 6y = 15
⇒ 12y = 0
⇒ y = 0
Substituting the value of y in equation (iii), we get:
x = 2(0) + 5
⇒ x = 5
Therefore, the solution of the given pair of equations is (5, 0).
Since we have obtained a unique solution for the given pair of equations, the correct option is (A).
However, the given answer is (C), which is incorrect. It seems like there is an error in the answer key.
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