State true or false.Solving the system of linear equations

2x−3y=1;3x−4y=1
graphically, we infer that the point (3, 2) lies on any of the lines.

Question

State true or false.Solving the system of linear equations

2x−3y=1;3x−4y=1
   graphically, we infer that the point (3, 2) lies on any of the lines.

Accepted Answer

Given pair of linear equations is

2x−3y=1;3x−4y=1
  .

2x - 3y = 1

⇒2x - 3y - 1 = 0                        ......(1)

3x - 4y = 1

⇒3x - 4y - 1 = 0                        ......(2)

From (1),

2x−3y=1

⇒3y=2x−1

⇒y=
      
       2x−1
      3

From equation 1,

y = 
    
     2x−1
    3

, table for

2x - 3y - 1 = 0 
   is given by,So, the points are

0.5,0
   ,
    
     0,−0.33
   
   and

3,2
   
  .From (2),

3x−4y=1

⇒4y=3x−1

⇒y=
      
       3x−1
      4

From equation 1,

y = 
    
     3x−1
    4

, table for

3x - 4y - 1 = 0 
  is given by,So, the points are

0,−0.25
   ,
    
     0.33,0
   and
    
     −1,−1
   
  .On plotting points

0.5,0
   ,
    
     0,−0.33
   
  and

3,2
   
   and

0,−0.25
   ,
    
     0.33,0
   
   and

−1,−1
   
   on the following graph which is produced when the aforementioned equations are written on the graph paper and connected by a line. In the graph, we observed that these two lines intersect at point F (- 1, - 1). As a result, we have the following equation's graphical representation. Hence, (- 1, - 1) is the solution of the given equations. Yes, point (3, 2) lies on the equation

2x - 3y = 1 or 2x - 3y - 1 = 0 
  . Therefore, the statement is true.Thus, option 1 is correct.

State true or false.

Solving the system of linear equations $2 x − 3 y = 1; 3 x − 4 y = 1$ graphically, we infer that the point (3, 2) lies on any of the lines.

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State true or false.Solving the system of linear equations 2x−3y=1;3x−4y=1 graphically, we infer that the point (3, 2) lies on any of the lines.