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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?
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Verified Answer
The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:a)A u...
Here,
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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
Most Upvoted Answer
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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Community Answer
The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:a)A u...
If we solve that linear equations in two variables we will get -3,-3,-3
by the rule of consistency which is a1/a2=b1/b2=c1/c2 that's why it had infinitely many solutions
by the rule of consistency which is a1/a2=b1/b2=c1/c2 that's why it had infinitely many solutions
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