form a question of assertion and reasoning of linear equation of two variables
Answers
Answer:
Assertion: Homogeneous system of linear equations is always consistent.
Reason:x=0,y=0
is always a solution of the homogeneous systeof equations with unknowns x and y then which of the following statements is true?
A.Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B.Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C.Assertion is correct but Reason is incorrect.
D.Assertion is incorrect but Reason is correct
Answer :option A is the correct option
.
Answer:
We know that the general equation of a Homogeneous system of linear equations with two variables in it is ax+by=0
.
At the point (0,0)
, the equation is always consistent as this point is always the solution of the linear equation.
⇒a(0)+b(0)=0
By solving the above equation we get
⇒0=0
i.e. LHS is equal to the RHS of the equation.
So we can clearly see that x=0,y=0
is always a solution of the homogeneous system of equations with unknowns x
and y
.
Hence the Assertion is correct with the reason as its correct explanation.