Karnataka SSLC (Class 10) Linear Equations in One Variable — practice questions — page 2

Explore 33 free Linear Equations in One Variable questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Equations in One Variable questions and exercises with answers

Showing questions 31–33 of 33.

CLASS10 · Mathematics · Linear Equations — ConsistencyRead the answer and worked solution →If the two lines of a pair of linear equations are coincident (same line), the pair hasRead the answer and worked solution →A pair of linear equations that has at least one solution is said to beRead the answer and worked solution →

Worked practice questions

CLASS10 · Mathematics · Linear Equations — Consistency

Read exercise and reference answers

Items

Item
Lines intersect at exactly one point
Answer
left
Item
Parallel lines
Answer
right
Item
a₁/a₂ ≠ b₁/b₂
Answer
left
Item
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Answer
right
Item
Unique x, y satisfy both equations
Answer
left
Item
Graphs never meet
Answer
right

Categories

Left: Consistent (one solution)
Right: Inconsistent (no solution)

Instructions

Classify each scenario: consistent or inconsistent system?

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If the two lines of a pair of linear equations are coincident (same line), the pair has

no solution
a unique solution
infinitely many solutions
two solutions

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Correct answer: C. infinitely many solutions

1. Coincident lines lie exactly on top of each other. 2. Every point on the line satisfies both equations, so there are **infinitely many solutions**. 3. Their coefficients satisfy a₁/a₂ = b₁/b₂ = c₁/c₂. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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A pair of linear equations that has at least one solution is said to be

inconsistent
parallel
undefined
consistent

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Correct answer: D. consistent

1. Pairs are classified by whether a solution exists. 2. A pair with one or more solutions is **consistent** (intersecting or coincident lines). 3. A pair with no solution is inconsistent (parallel lines). _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

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