Linear Equations in Two Variables: 9 Math
NCERT Exercise 4.1: 9th math
In this chapter we will learn to solve the question based on Linear Equation in Two Variables. In this NCERT Exercise 4.1, class ninth math, we will learn to express a given linear equation in two variables in its standard form ax + bx + c = 0 and find the values of a, b, and c.
Question (1) 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)
Solution:
Let the cost of a notebook = x
And the cost of a pen = y
[Here, two variables has been taken, first for the notebook = x, and second for the pen = y]
Thus, according to question,
Cost of a notebook = twice the cost of a pen
⇒ Cost of a notebook = 2 × cost of a pen
⇒ x = 2 y
⇒ x – 2 y = 0
Thus, the linear equation for the given situation is "x = 2 y" or "x – 2 y = 0" Answer
Question (2) 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) 2 x + 3 y = 9.35
Solution
Given equation is
2 x + 3 y = 9.35
Thus, by transposing the constant term 9.35 situated at RHS to the LHS of the equation, we get
2 x + 3 y – 9.35 = 0
⇒ 2 x + 3 y + (– 9.35) = 0
So, it is the given linear equation in two variables in the form of a x + by + c
The coefficient of terms in the above linear equation in two variables can be depicted as follows:
2 x +/↑ /a x +3 y +/↑ /b y +(– 9.35) = 0/↑ /c
Thus, in this equation,
"a", the co-efficient of x = 2,
"b", the co-efficient of y = 3, and
"c", the constant term = – 9.35 = 0
Thus, the required form of the linear equation in two variables for the given situation is
2 x + 3 y + (– 9.35) = 0, in which a = 2, b = 3, and c = 9.35 = 0 Answer
Question (2) (ii) x – y/5 – 10 = 0
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given, equation is x – y/5 – 10 = 0
This equation is already in the form of a x + b x + c = 0
And, this equation can be written in the required form as given below
x + (– y/5) + (– 10) = 0
The above equation can be written as given also below to understand the coefficient of x, y, and constant term.
1 × x + (– 1/5) × y + (– 10) = 0
Thus, in this equation,
The coefficient of "x" = a = 1
The coefficient of "y" = b = – 1/5
And constant term "c" = 10
Thus, the given equation in the form of ax + by + c = 0 is
x + (– y/5) + (– 10) = 0, and "a = 1, b = – 1/5 , and c = 10" Answer
Question (2) (iii) 2x + 3y = 6
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is 2x + 3y = 6
By transposing "6" to the LHS, we get
⇒ 2x + 3y – 6 = 0
⇒ 2x + 3y + (– 6) = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 2
The coefficient of y or the value of "b" = 3, and
The value of constant term "c" = – 6
Thus, the given equation is in the form of ax + by + c = 0 is
2x + 3y + (– 6) = 0 and the values of a = 2, b = 3 and c = – 6 Answer
Question (2) (iv) x = 3y
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is x = 3y
By transposing "3y" to the LHS, we get
⇒ x – 3y = 0
This equation can be expressed in the form of ax + by + c = 0 as follows:
x + (– 3y) + 0 = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 1
The coefficient of y or the value of "b" = – 3, and
The value of constant term "c" = 0
Thus, the given equation is in the form of ax + by + c = 0 is
x + (– 3y) + 0 = 0 and the values of a = 1, b = – 3 and c = 0 Answer
Question (2) (v) 2x = – 5y
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is 2x = – 5y
By transposing "– 5y" to the LHS, we get
2x + 5y = 0
This equation can be expressed in the form of ax + by + c = 0 as follows:
2x + 5y + 0 = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 2
The coefficient of y or the value of "b" = 5, and
The value of constant term "c" = 0
Thus, the given equation is in the form of ax + by + c = 0 is
2x + 5y + 0 = 0 and the values of a = 2, b = 5 and c = 0 Answer
Question (2) (vi) 3x + 2 = 0
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is 3x + 2 = 0
This equation can be expressed in the form of ax + by + c = 0 as follows:
3x + 0.y + 2 = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 3
The coefficient of y or the value of "b" = 0, and
The value of constant term "c" = 2
Thus, the given equation is in the form of ax + by + c = 0 is
3x + 0.y + 2 = 0 and the values of a = 3, b = 0 and c = 2 Answer
Question (2) (vii) y – 2 = 0
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is y – 2 = 0
This equation can be expressed in the form of ax + by + c = 0 as follows:
0.x + y + (– 2) = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 0
The coefficient of y or the value of "b" = 1, and
The value of constant term "c" = – 2
Thus, the given equation is in the form of ax + by + c = 0 is
0.x + y + (– 2) = 0 and the values of a = 0, b = 1 and c = – 2 Answer
Question (2) (viii) 5 = 2x
[Express the given linear equations in the form ax + by + c = 0 and indicate the values of a, b and c]
Solution
Given linear equation is 5 = 2x
After transposing 5 to RHS, we get
0 = 2x – 5
After rearranging the above equation, we get
2x – 5 = 0
This equation can be expressed in the form of ax + by + c = 0 as follows:
2x + 0.y + (– 5) = 0
After comparing this linear equation with ax + by + c =0, we get
The coefficient of x or the value of "a" = 2
The coefficient of y or the value of "b" = 0, and
The value of constant term "c" = – 5
Thus, the given equation is in the form of ax + by + c = 0 is
2x + 0.y + (– 5) = 0 and the values of a = 2, b = 0 and c = – 5 Answer
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