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Standard VII

Mathematics

Introduction to Algebra

Assertion :Ho...

Question

Assertion :Homogeneous system of linear equations is always consistent. Reason: $x = 0, y = 0$ is always a solution of the homogeneous system of equations with unknowns x and y, then which of the following statement is true?

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Any homogeneous linear equation(2 variable) will be of the form $a x + b y = 0$ .
And $(0, 0)$ will always be solution of this.
So, Assertion is correct and reason is it's correct explanation.

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Assertion :Homogeneous system of linear equations is always consistent. Reason: x=0,y=0 is always a solution of the homogeneous system of equations with unknowns x and y, then which of the following statement is true?

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionAny homogeneous linear equation(2 variable) will be of the form ax+by=0.And (0,0) will always be solution of this.So, Assertion is correct and reason is it's correct explanation.

Assertion :Homogeneous system of linear equations is always consistent. Reason: $x = 0, y = 0$ is always a solution of the homogeneous system of equations with unknowns x and y, then which of the following statement is true?