Assertion (A): The system $x + 2y = 3$ , $2x + 4y = 6$ has infinitely many solutions.
Reason (R): Whenever $|A| = 0$ , the system $AX = B$ has infinitely many solutions.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The second equation is exactly twice the first, so every solution of one solves the other: A is true.
R is false: $x + 2y = 3$ , $2x + 4y = 7$ also has $|A| = 0$ but no solution at all.

Concept: Conditions for infinitely many solutions
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsConsistency of a system of equations

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Ten questions from Determinants, Adjoint & Inverse, at your own pace.

Assertion (A): The system x+2y=3x + 2y = 3x+2y=3, 2x+4y=62x + 4y = 62x+4y=6 has infinitely many solutions.Reason (R): Whenever ∣A∣=0|A| = 0∣A∣=0, the system AX=BAX = BAX=B has infinitely many solutions.

Explanation

Assertion (A): The system $x + 2y = 3$ , $2x + 4y = 6$ has infinitely many solutions.
Reason (R): Whenever $|A| = 0$ , the system $AX = B$ has infinitely many solutions.