Which solution status is correct for (x+2y=3) and (4x+8y=12)?
Answer and explanation
Correct answer: Infinitely many solutions
For a pair of linear equations, compare the corresponding coefficients and constants. Multiplying x+2y=3 by 4 gives 4x+8y=12, exactly the second equation. Thus both equations represent the same straight line, and every point on that line satisfies both equations. Therefore infinitely many ordered pairs are solutions. A unique solution would require intersecting lines, while parallel distinct lines would give no solution.
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What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
For a pair of linear equations, compare the corresponding coefficients and constants. Multiplying x+2y=3 by 4 gives 4x+8y=12, exactly the second equation. Thus both equations represent the same straight line, and every point on that line satisfies both equations. Therefore infinitely many ordered pairs are solutions. A unique solution would require intersecting lines, while parallel distinct lines would give no solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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