Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma Solutions: Linear Equations in Two Variables- 1
Linear Equations in Two Variables- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download
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Page 1
Question:1
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 = 12
ii
x -
y
2
-5 = 0
iii
2x + 3y = 9.35
iv
3x = -7y
v
2x + 3 = 0
vi
y - 5 = 0
vii
4 = 3x
viii
y =
x
2
Solution:
i We are given
-2x + 3y - 12 = 0
Comparing the given equation with ,we get
a = -2; b = 3; c = -12
i i We are given
Comparing the given equation with ,we get
i i i We are given
Comparing the given equation with ,we get
Page 2
Question:1
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 = 12
ii
x -
y
2
-5 = 0
iii
2x + 3y = 9.35
iv
3x = -7y
v
2x + 3 = 0
vi
y - 5 = 0
vii
4 = 3x
viii
y =
x
2
Solution:
i We are given
-2x + 3y - 12 = 0
Comparing the given equation with ,we get
a = -2; b = 3; c = -12
i i We are given
Comparing the given equation with ,we get
i i i We are given
Comparing the given equation with ,we get
i v We are given
Comparing the given equation with ,we get
v We are given
Comparing the given equation with ,we get
v i We are given
Comparing the given equation with ,we get
v i i We are given
Comparing the given equation with ,we get
v i i i We are given
Comparing the given equation with ,we get
Question:2
Write each of the following as an equation in two variables:
i
2x =-3
ii
y = 3
iii
5x =
7
2
iv
Page 3
Question:1
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 = 12
ii
x -
y
2
-5 = 0
iii
2x + 3y = 9.35
iv
3x = -7y
v
2x + 3 = 0
vi
y - 5 = 0
vii
4 = 3x
viii
y =
x
2
Solution:
i We are given
-2x + 3y - 12 = 0
Comparing the given equation with ,we get
a = -2; b = 3; c = -12
i i We are given
Comparing the given equation with ,we get
i i i We are given
Comparing the given equation with ,we get
i v We are given
Comparing the given equation with ,we get
v We are given
Comparing the given equation with ,we get
v i We are given
Comparing the given equation with ,we get
v i i We are given
Comparing the given equation with ,we get
v i i i We are given
Comparing the given equation with ,we get
Question:2
Write each of the following as an equation in two variables:
i
2x =-3
ii
y = 3
iii
5x =
7
2
iv
y =
3
2
x
Solution:
i We are given,
Now, in two variable forms the given equation will be
i i We are given,
Now, in two variable forms the given equation will be
i i i We are given,
Now, in two variable forms the given equation will be
i v We are given,
Now, in two variable forms the given equation will be
Question:3
The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in
two variables.
Solution:
Let the cost of fountain pen be x and cost of ball pen be y.
According to the given equation, we have
Here x is the cost of one fountain pen and y is that of one ball pen.
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FAQs on Linear Equations in Two Variables- 1 RD Sharma Solutions - Mathematics (Maths) Class 9
| 1. What is a linear equation in two variables? |  |
Ans. A linear equation in two variables is an equation of the form ax + by = c, where a, b, and c are constants and x and y are variables. It represents a straight line on a coordinate plane.
| 2. How do we solve a linear equation in two variables? | |
Ans. To solve a linear equation in two variables, we need to find the values of the variables that satisfy the equation. This can be done using various methods like substitution, elimination, or graphical representation.
| 3. Can a linear equation in two variables have more than one solution? | |
Ans. Yes, a linear equation in two variables can have more than one solution. In fact, there can be infinitely many solutions depending on the equation. For example, the equation 2x + 3y = 6 has infinitely many solutions.
| 4. How do we represent a linear equation in two variables graphically? | |
Ans. To represent a linear equation in two variables graphically, we plot the points that satisfy the equation on a coordinate plane and then join these points to form a straight line. The line represents all the solutions to the equation.
| 5. Can a linear equation in two variables have no solution? | |
Ans. Yes, a linear equation in two variables can have no solution. This happens when the graph of the equation is parallel to the x-axis and y-axis and does not intersect. In such cases, the equation is said to be inconsistent.
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