If two lines have different slopes then how many solutions will the pair have?
Answer and explanation
Correct answer: One unique solution
The slope of a nonvertical line describes how much its y-value changes when its x-value changes. Lines with different slopes have different directions, so they cannot remain parallel or overlap completely. In a plane, two such lines meet at exactly one point. That point gives one ordered pair satisfying both linear equations. Therefore, a pair represented by lines with unequal slopes is called consistent and independent and has one unique solution.
To see the algebraic meaning, different slopes imply that the equations are not scalar multiples with equal coefficient ratios. The two lines therefore cannot describe the same line, and they cannot be distinct parallel lines, because parallel lines have equal slopes. They must intersect once. Hence the number of common solutions is one, which is option C. Infinite solutions correspond to coincident lines, while no solution corresponds to distinct parallel lines.
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
The slope of a nonvertical line describes how much its y-value changes when its x-value changes. Lines with different slopes have different directions, so they cannot remain parallel or overlap completely. In a plane, two such lines meet at exactly one point. That point gives one ordered pair satisfying both linear equations. Therefore, a pair represented by lines with unequal slopes is called consistent and independent and has one unique solution.
To see the algebraic meaning, different slopes imply that the equations are not scalar multiples with equal coefficient ratios. The two lines therefore cannot describe the same line, and they cannot be distinct parallel lines, because parallel lines have equal slopes. They must intersect once. Hence the number of common solutions is one, which is option C. Infinite solutions correspond to coincident lines, while no solution corresponds to 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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