The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(A) a unique solution (B) exactly two solutions
(C) infinitely many solutions (D) no solution
NCERT Class X
Mathematics - Exemplar Problems
Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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Given :
equation 1 :- x + 2y + 5 = 0
equation 2 :- –3x – 6y + 1 = 0
To find :
Number of solutions
Solution :
Solving equation (1) and (2)
multiply equation (1) by 3
3×(x + 2y + 5) = 0
3x + 6y + 15 = 0
Add equation (1) and (2)
3x + 6y + 15 + (–3x – 6y + 1) = 0
16 is not equal to 0
• Hence, there is no such value of x and y for which two lines intersect or we can say that given lines are parallel to each other.
• Option D is correct
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