Which statement is correct about the graph of the equations (18x+24y=54) and (3x+4y=11)?
Answer and explanation
Correct answer: Lines are distinct parallel
To classify two linear equations graphically, compare the ratios of corresponding coefficients. If the ratios of the coefficients of \(x\) and \(y\) are equal but the ratio of the constants is different, the equations represent distinct parallel lines. Such lines have the same direction but lie at different positions, so they never meet.
For these equations, \(18/3=6\) and \(24/4=6\), so the variable coefficients are proportional. However, \(54/11\ne6\). Therefore the constant terms do not have the same proportion. The lines are parallel but not coincident, and the pair has no common solution. Thus the correct graph description is option C, distinct parallel lines.
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What is the correct answer to this question?
Lines are distinct parallel
Why is this the correct answer?
To classify two linear equations graphically, compare the ratios of corresponding coefficients. If the ratios of the coefficients of \(x\) and \(y\) are equal but the ratio of the constants is different, the equations represent distinct parallel lines. Such lines have the same direction but lie at different positions, so they never meet.
For these equations, \(18/3=6\) and \(24/4=6\), so the variable coefficients are proportional. However, \(54/11\ne6\). Therefore the constant terms do not have the same proportion. The lines are parallel but not coincident, and the pair has no common solution. Thus the correct graph description is option C, distinct parallel lines.
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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