Elimination methodPractice Questions & MCQs

Q1. If elimination yields 0 = 0, the system has (NCERT):

• A.infinitely many solutions
• B.two solutions
• C.a unique solution
• D.no solution

Answer: A. infinitely many solutions

Reading the problem, 0, 0 (math, chapter 'Pair of Linear Equations'). What we must find: the requested quantity. This is a classic application of hence the required answer = infinitely many solutions. Set up the relation specified by the stem (formula / theorem from the relevant Class-10 chapter) and substitute the listed numerical data. Matching this against the options, A) infinitely many solutions is the answer. As for the others, option B) 'two solutions' is incorrect: Infinitely many; option C) 'a unique solution' is wrong because 0=0 means dependent equations.

Q2. If elimination yields 0 = 7, the system has (NCERT):

• A.x = 7
• B.a unique solution
• C.no solution
• D.infinitely many

Answer: C. no solution

First, read what's there - a typical math numerical. The data on the table: 0, 7. We are after the quantity the stem asks for. Tool of choice - hence the required answer = no solution. Rearrange it for the unknown before substituting. Common-sense check: set up the relation specified by the stem (formula / theorem from the relevant Class-10 chapter) and substitute the listed numerical data. Lock in option C) no solution. Trap-watch: option A) 'x = 7' fails since 0=7 is impossible => no solution; option B) 'a unique solution' is incorrect: A false statement => inconsistent.

Q3. Solve 2x + y = 7 and 3x - y = 8; the value of x is (NCERT):

• A.1
• B.4
• C.2
• D.3

Answer: D. 3

Given 2, 7, 3, 8, asked for the unknown. By hence the required answer = 3. hence the required answer = 3. set up the relation specified by the stem (formula / theorem from the relevant Class-10 chapter) and substitute the listed numerical data. Thus option D) 3. Others fail: option A) '1' fails since Add equations: 5x=15 => x=3; option C) '2' fails since x = 3, y = 1.