Find the best tutors and institutes for Class 10 Tuition
Q2(v):
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case:
(v) $2x = -5y$
Solution :
Initial Setup & Theoretical Foundation
We are given the linear equation:
$2x = -5y$
The objective is to express this equation in the general (standard) form of a linear equation in two variables, which is defined as:
$ax + by + c = 0$
where $a$, $b$, and $c$ are real numbers, and $a$ and $b$ are not both zero simultaneously (i.e., $a^2 + b^2 \neq 0$).
Step 1: Algebraic Transposition
To convert the given equation into the standard form, all non-zero terms must be collected on the left-hand side (LHS) of the equation, leaving zero on the right-hand side (RHS).
We apply the Addition Property of Equality [which states that adding the same quantity to both sides of an equation preserves the equality]. We add $5y$ to both sides of the equation:
$2x + 5y = -5y + 5y$
$2x + 5y = 0$
Step 2: Structuring the Standard Form
The standard form requires three distinct terms: an $x$-term, a $y$-term, and a constant term $c$. In our current equation, $2x + 5y = 0$, the constant term is absent. Mathematically, an absent term implies a coefficient or value of zero. We explicitly introduce zero as the constant term to perfectly match the $ax + by + c = 0$ template:
$2x + 5y + 0 = 0$
Step 3: Coefficient Extraction
By directly comparing our structured equation with the general form $ax + by + c = 0$, we can extract the corresponding real number coefficients:
- The coefficient of $x$ corresponds to $a$. Thus, $a = 2$.
- The coefficient of $y$ corresponds to $b$. Thus, $b = 5$.
- The constant term corresponds to $c$. Thus, $c = 0$.
Graphical Representation (Geometric Interpretation)
A linear equation in two variables geometrically represents a straight line on a Cartesian plane. Because the constant term $c = 0$, the line must pass through the origin $(0,0)$. We can verify this by finding two points that satisfy $2x + 5y = 0$:
- If $x = 0$, then $5y = 0 \implies y = 0$. Point: $(0, 0)$
- If $x = 5$, then $10 + 5y = 0 \implies 5y = -10 \implies y = -2$. Point: $(5, -2)$
- If $x = -5$, then $-10 + 5y = 0 \implies 5y = 10 \implies y = 2$. Point: $(-5, 2)$
Final Solution: The linear equation expressed in standard form is $2x + 5y + 0 = 0$. The corresponding coefficient values are $a = 2$, $b = 5$, and $c = 0$.
More Questions from Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.1
- Q1: The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be $x$ and that of a pen to be $y$).
- Q2(i): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (i) $2x + 3y = 9.3\overline{5}$
- Q2(ii): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (ii) $x - \frac{y}{5} - 10 = 0$
- Q2(iii): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (iii) $-2x + 3y = 6$
- Q2(iv): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (iv) $x = 3y$
- Q2(vi): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (vi) $3x + 2 = 0$
- Q2(vii): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (vii) $y - 2 = 0$
- Q2(viii): Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (viii) $5 = 2x$
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
Super Tutor
Sector 5, Dwarka, Delhi
10 yrs of
Exp
11 students
1233 hrs of classes completed
600
per hour
Online Classes
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.
Top Tutor
Ashok Nagar D' Souza Layout, Bangalore
10 yrs of
Exp
25 students
772 hrs of classes completed
600
per hour
Online Classes
10+ years of experience teaching Mathematics for Grades 10 to 12th • Consistent record of 100% academic results • Very friendly and supportive learning environment • Encourages students to ask questions freely and confidently • Strong focus on conceptual clarity and problem-solving skills • Helps students build confidence and excel in Mathematics • Fee Structure for One-to-One Classes: ₹700 per hour • Group Classes: ₹4,000 per month.
Sir clears all my doubts he makes difficult concepts easy to understand he takes Previous year questions which makes it easier to prepare
Top Tutor
Kurichimuttom, Kozhencherry
7 yrs of
Exp
4 students
379 hrs of classes completed
350
per hour
Online Classes
I have taught almost 50 students.
The best teacher my daughter have ever got. She can understand everything that she took and also did many question papers. She could write everything that her teacher teaches her and the teacher is very lovely.
Top Tutor
MSR nagar mathikere, Bangalore
20 yrs of
Exp
21 students
5437 hrs of classes completed
499
per hour
Online Classes
I enjoy teaching and making things easier and fun for the children. Didn't send my kids for any tuitions. Today the elder child is a CSE graduate , working for Amazon & the other is in her 3rd year MBBS !
I have been studying Maths and Science under her guidance since 8th grade. She explains every concept in a simple and clear way, making even difficult topics easy to understand. Her teaching style is patient and supportive, and she always makes sure all doubts are cleared. She focuses on strengthening basics and gives regular practice, which has really helped me improve. Because of her guidance, my confidence in both subjects has increased a lot. I am truly grateful for her dedication and support
Top Tutor
Asilmetta, Visakhapatnam
3 yrs of
Exp
Online Classes
Student's Home
Tutor's home
Seeing my students succeed is the best reward! I bring lessons to life with real-world examples, and I put my all into every class. It's amazing to watch them not only understand the material but also get excited about learning. Their good grades are definitely a confidence booster!
Find more Tutor for Linear Equations in Two Variables in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.1 worksheets
Download Now
