Which statement is correct about the graph of the equations (20x+30y=90) and (2x+3y=11)?
Answer and explanation
Correct answer: Lines are distinct parallel
When the ratios of the coefficients of \(x\) and \(y\) are equal, the two lines have the same slope. To decide whether they are the same line or distinct parallel lines, compare the ratio of the constants too. Equal ratios throughout mean coincident lines; a different constant ratio means distinct parallel lines.
Here, \(20/2=10\) and \(30/3=10\), but \(90/11\ne10\). Thus the coefficients of the variables are proportional, while the constants are not. The equations represent two separate parallel lines. They have no common point, so the graph is of distinct parallel lines, as stated in option C.
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What is the correct answer to this question?
Lines are distinct parallel
Why is this the correct answer?
When the ratios of the coefficients of \(x\) and \(y\) are equal, the two lines have the same slope. To decide whether they are the same line or distinct parallel lines, compare the ratio of the constants too. Equal ratios throughout mean coincident lines; a different constant ratio means distinct parallel lines.
Here, \(20/2=10\) and \(30/3=10\), but \(90/11\ne10\). Thus the coefficients of the variables are proportional, while the constants are not. The equations represent two separate parallel lines. They have no common point, so the graph is of distinct parallel lines, as stated in option C.
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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