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Linear Equations in Two Variables- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

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Question:4
Write two solutions for each of the following equations:
Page 2


  
   
         
   
         
   
         
   
         
                        
 
              
      
                
Question:4
Write two solutions for each of the following equations:
i
3x + 4y = 7
ii
x = 6y
iii
x + xy = 4
iv
2
3
x -y = 4
Solution:
i We are given,
Substituting x = 1 in the given equation, we get
Substituting x = 2 in the given equation, we get
i i We are given,
Substituting in the given equation, we get
Substituting in the given equation, we get
i i i We are given,
Page 3


  
   
         
   
         
   
         
   
         
                        
 
              
      
                
Question:4
Write two solutions for each of the following equations:
i
3x + 4y = 7
ii
x = 6y
iii
x + xy = 4
iv
2
3
x -y = 4
Solution:
i We are given,
Substituting x = 1 in the given equation, we get
Substituting x = 2 in the given equation, we get
i i We are given,
Substituting in the given equation, we get
Substituting in the given equation, we get
i i i We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 4 in the given equation, we get
i v We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 3 in the given equation, we get
Question:5
Check which of the following are solutions of the equations 2x - y = 6 and which are not:
i
3, 0
ii
0, 6
iii
2, -2
iv
v
3, 0
( )
Page 4


  
   
         
   
         
   
         
   
         
                        
 
              
      
                
Question:4
Write two solutions for each of the following equations:
i
3x + 4y = 7
ii
x = 6y
iii
x + xy = 4
iv
2
3
x -y = 4
Solution:
i We are given,
Substituting x = 1 in the given equation, we get
Substituting x = 2 in the given equation, we get
i i We are given,
Substituting in the given equation, we get
Substituting in the given equation, we get
i i i We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 4 in the given equation, we get
i v We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 3 in the given equation, we get
Question:5
Check which of the following are solutions of the equations 2x - y = 6 and which are not:
i
3, 0
ii
0, 6
iii
2, -2
iv
v
3, 0
( )
v
1
2
, -5
Solution:
We are given,
2x – y = 6
i In the equation 2x – y = 6,we have
Substituting x = 3 and y = 0 in 2x – y, we get
is the solution of 2x – y = 6.
 
i i In the equation 2x – y = 6, we have
Substituting x = 0 and y = 6 in 2x – y,we get
is not the solution of 2x – y = 6.
 
i i i In the equation 2x – y = 6,we have
Substituting x = 2 and y = –2  in 2x – y, we get
is the solution of 2x – y = 6.
 
i v In the equation 2x – y = 6, we have
Substituting  and y = 0 in 2x – y, we get
is not the solution of 2x – y = 6.
 
v In the equation 2x – y = 6, we have
( )
Page 5


  
   
         
   
         
   
         
   
         
                        
 
              
      
                
Question:4
Write two solutions for each of the following equations:
i
3x + 4y = 7
ii
x = 6y
iii
x + xy = 4
iv
2
3
x -y = 4
Solution:
i We are given,
Substituting x = 1 in the given equation, we get
Substituting x = 2 in the given equation, we get
i i We are given,
Substituting in the given equation, we get
Substituting in the given equation, we get
i i i We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 4 in the given equation, we get
i v We are given,
Substituting x = 0 in the given equation, we get
Substituting x = 3 in the given equation, we get
Question:5
Check which of the following are solutions of the equations 2x - y = 6 and which are not:
i
3, 0
ii
0, 6
iii
2, -2
iv
v
3, 0
( )
v
1
2
, -5
Solution:
We are given,
2x – y = 6
i In the equation 2x – y = 6,we have
Substituting x = 3 and y = 0 in 2x – y, we get
is the solution of 2x – y = 6.
 
i i In the equation 2x – y = 6, we have
Substituting x = 0 and y = 6 in 2x – y,we get
is not the solution of 2x – y = 6.
 
i i i In the equation 2x – y = 6,we have
Substituting x = 2 and y = –2  in 2x – y, we get
is the solution of 2x – y = 6.
 
i v In the equation 2x – y = 6, we have
Substituting  and y = 0 in 2x – y, we get
is not the solution of 2x – y = 6.
 
v In the equation 2x – y = 6, we have
( )
Substituting  and y = –5 in 2x – y, we get
is the solution of 2x – y = 6.
Question:6
If x = -1, y = 2 is a solution of the equation 3x + 4y = k, find the value of k.
Solution:
We are given,
is the solution of equation .
Substituting  and  in ,we get
Question:7
Find the value of ?, if x  = - ? and y = 
5
2
is a solution of the equation x + 4y - 7 = 0.
Solution:
We are given,
is the solution of equation .
Substituting  and  in ,we get
Question:8
If x = 2 a + 1 and y = a - 1 is a solution of the equation 2x - 3y + 5 = 0, find the value of a .
Solution:
We are given,
is the solution of equation .
Substituting  and  in ,we get
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FAQs on Linear Equations in Two Variables- 2 RD Sharma Solutions - Mathematics (Maths) Class 9

1. What are linear equations in two variables?
Ans. Linear equations in two variables are equations that involve two variables and can be written in the form ax + by + c = 0, where a, b, and c are constants. These equations represent straight lines on a coordinate plane.
2. How do you 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. We can do this by using various methods such as substitution method, elimination method, or graphical method. These methods involve manipulating the equations to isolate one variable and then substituting its value into the other equation to find the value of the remaining variable.
3. Can a linear equation in two variables have more than one solution?
Ans. Yes, a linear equation in two variables can have infinitely many solutions. This happens when the two equations are the same or when they represent the same line on a coordinate plane. In such cases, any point on the line will satisfy both equations and thus be a solution to the system of equations.
4. How do you graph a linear equation in two variables?
Ans. To graph a linear equation in two variables, we need to plot the points that satisfy the equation and then connect them to form a straight line. We can do this by finding the x and y intercepts of the equation or by using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
5. What is the importance of linear equations in two variables?
Ans. Linear equations in two variables are important in various fields such as physics, economics, and engineering. They help us model and solve real-life problems that involve two related variables. By finding solutions to these equations, we can determine the relationship between the variables and make predictions or analyze the behavior of the system under different conditions.
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