Explain the unique solution,no solution or infinite solutions
Class 10th rd sharma pair of linear equations in two variables.
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In each of the following systems of equations, determine whether the system has a unique solution, no solution or infinite solutions. In case there is a unique solution, find it from 1 to 4. 1. x − 3y = 3 3x − 9y = 2
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Solution:
The given system of equations is
x − 3y – 3 = 0
3x − 9y − 2 = 0
The above equations are of the form
a1 x + b1 y − c1 = 0
a2 x + b2 y − c2 = 0
Here, a1 = 1, b1 = −3, c1 = −3
a2 = 3, b2 = −9, c2 = −2
So, according to the question, we get
a1 / a2 = 1/3
b1 / b2 = −3/ −9 = 1/3 and,
c1 / c2 = −3/ −2 = 3/2
⇒ a1 / a2 = b1/ b2 ≠ c1 / c2
Hence, we can conclude that the given system of equations has no solution.