CAT Linear Equations section is the part of algebra and candidates can expect around 1-2 questions from this topic. As per the previous year's analysis of CAT question paper, the difficulty level of questions asked from the algebra had been rated moderate. With regular practice and right knowledge of basic concepts of linear equations i.e. 1-Variable, 2-Variable and 3-Variable equations etc you can easily solve the questions based on this concept. Also Check CAT QA Syllabus
In CAT 2021, candidates can expect the questions from Linear Equations to be merged with other concepts or topics like Maximum, Minimum, Roots of Equation, Real and Imaginary Roots. Therefore the in depth preparation of the topic is required. In the article below, we have provided the basic concepts of linear equation along with important formulas and solved sample questions.
Linear equations is a mathematical statement that has an equal to the symbol of "=". In linear equations where each term contains an exponent of one. Also, after the graphing of the equation, a straight line can be seen. It is an equation where the equation of degree is 1. And it can be written for two different variables. Also, it is a combination of two variables.
Types of Linear Equations:
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In the below section, some of the basic and important formulas of CAT Linear Equations are mentioned.
Term | Formula |
---|---|
Linear Equation in One Variable | ax + b = 0 a ≠ 0 and x is the variable |
Linear Equation in Two Variable | ax + by + c = 0 a ≠ 0, b ≠ 0 , x and y are the variables |
Linear Equation in Three Variable | ax + by + cz + d = 0 a ≠ 0, b ≠ 0, c ≠ 0, x, y, z are the variables |
Slope Intercept Form | y = mx + b m = slope of the line b = y intercept |
Point Slope Form | y – y1 = m(x – x1 ) |
In the section below, some solved questions of CAT Linear Equations of the previous year are mentioned below.
Ques. 3x + 4|y| = 33. What is the number of integer values of (x, y) possible?
Correct Answer: ( 4 )
Ques. (|x| - 3) (|y| + 4) = 12. What is the number of pairs of integers (x, y) that proves this equation?
Correct Answer: ( 3 )
Ques. x + |y| = 8, |x| + y = 6. What is the number of pairs of x, y that proves these two equations?
Correct Answer: ( 4 )
Ques. How many real solutions of the equation are there in x2 - 7|x| - 18 = 0 ?
Correct Answer: ( 1 )
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Ques. x2 - 9x + |k| = 0 has real roots. What are the number of integer values can 'k' take?
Correct Answer: ( 4 )
Ques. x2 - 11x + |p| = 0 has integer roots. What are the number of integer values can 'p' take?
Correct Answer: ( 4 )
Ques. 2x + 5y = 103. How many pairs of positive integers x and y that satisfy the equation?
Correct Answer: ( 2 )
Ques. Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Where Median (a,b,c) - Mean (a,b,c) = 2. What will be the median of a, b, and c?
Correct Answer: ( 3 )
Ques. Equation x2 + 5x – 7 = 0 contains roots both a and b and Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. What will be the outcome of p + q?
Correct Answer: ( 3 )
Ques. What number of real solutions are there for the equation x2 – 7|x| - 30 = 0?
Correct Answer: ( 3 )
A list of important tips for the preparation of CAT Linear Equations are mentioned below.
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*The article might have information for the previous academic years, please refer the official website of the exam.