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Q4:
Find the value of $k$, if $x = 2$, $y = 1$ is a solution of the equation $2x + 3y = k$.
Solution :
Given Variables & Initial Setup
The problem provides a linear equation in two variables and a specific coordinate pair $(x, y)$ that satisfies the equation. The objective is to determine the unknown constant $k$.
- Linear Equation: $2x + 3y = k$
- Given Solution: $x = 2$
- Given Solution: $y = 1$
Step 1: Applying the Definition of a Solution
By definition, if $(x_0, y_0)$ is a solution to an equation, substituting these values into the equation must satisfy the equality [Per the Axiom of Substitution].
Substitute $x = 2$ and $y = 1$ into the given equation:
$2(2) + 3(1) = k$
Step 2: Arithmetic Evaluation
Perform the multiplication for both terms on the left-hand side (LHS):
$4 + 3 = k$
[By Arithmetic Addition]
$7 = k$
Step 3: Visual Representation (Coordinate Geometry)
The line $2x + 3y = 7$ passes through the point $(2, 1)$.
Step 4: Verification of Results
| Variable | Value |
|---|---|
| $x$ | 2 |
| $y$ | 1 |
| Equation Result | $2(2) + 3(1) = 7$ |
Final Solution: The value of $k$ is $7$.
More Questions from Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.2
- Q1: Which one of the following options is true, and why? $y = 3x + 5$ has
- Q2(i): Write four solutions for each of the following equations: (i) $2x + y = 7$
- Q2(ii): Write four solutions for each of the following equations: (ii) $\pi x + y = 9$
- Q2(iii): Write four solutions for each of the following equations: (iii) $x = 4y$
- Q3(i): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (i) $(0, 2)$
- Q3(ii): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (ii) $(2, 0)$
- Q3(iii): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (iii) $(4, 0)$
- Q3(iv): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (iv) $(\sqrt{2}, 4\sqrt{2})$
- Q3(v): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (v) $(1, 1)$
CBSE Solutions for Class 9 Mathematics Linear Equations in Two Variables
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Linear Equations in Two Variables
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Sector-16, Faridabad
1 yrs of
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4 students
532 hrs of classes completed
400
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I have taught my two sons when they were in class 10. They manged to clear the IIT JEE exam in 1st attempt. I teach by example, which helps the students to visualize the concepts and ideas. I believe in participative learning where the student also gives their viewpoints. This is how they start enjoying the subject and their performance level increases automatically.
My experience so far is great with Sir. He teaches topics very well. He also focuses on the practical applications of the topics.
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Sector 5, Dwarka, Delhi
10 yrs of
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15 students
1936 hrs of classes completed
600
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I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and same education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). This works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and same education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. -------------------------------------------------------------------------------Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have a one-to-one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. I will start the classes immediately once the first kid enrolls. -------------------------------------------------------------------------------I took classes and batches in different institutions.
The experience with virendra sir was amazing. He did away with all my doubts and difficulties at all times , he is more than a teacher and a mentor to me. I'll always remember sir's debate's , scolding and care for me. Ty sir for making me a greater individual.
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Sector 10, Dwarka, Delhi
20 yrs of
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4 students
114 hrs of classes completed
500
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Till date taught 1200+ students preparing for board examinations in 10th standard, average result= 98.75% marks. Do you want YOUR child to excel too? Contact me at the earliest!
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Chinsurah R S, Hooghly
15 yrs of
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7 students
987 hrs of classes completed
350
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I've taught at least 150 students of this Class till date ....online/offline together.
Very good teacher and friendly also. I have already join this sir's class. Very helpful teacher definitely. Thank you so much for your support. Highly recommended to all. Has good grip in the concept.
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Little Mount Saidapet, Chennai
Less than a yr
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3 students
266 hrs of classes completed
400
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CBSE Class 9 & 10 Math Expert | CEG & XLRI Alumnus | Multilingual Instruction About Me: High-quality mentorship matters most during the crucial transition of Classes 9 and 10. I am an engineer from College of Engineering, Guindy (1989) and a management alumnus from XLRI Jamshedpur (2004). What I Offer: Targeted CBSE Focus: Specialized coaching for 9th and 10th-grade Math to ensure top board exam results. Global Teaching Standards: Experienced in delivering high-impact math tutoring for students in North America (NAM) Multilingual Comfort: Instruction available in English, Tamil, Hindi, or Telugu to ensure zero communication barriers. I focus on building core conceptual foundations, rigorous practice, and exam-taking strategies. Let's work together to make Math your child's strongest subject!
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