State whether the following statement is true or false.

Point (-2, -5) is the solution of the linear equation $3 x - 5 y = 19 : - 7 x + 3 y + 1 = 0$ .

And point (4,9) lies on the linear equation $- 7 x + 3 y + 1 = 0$ .

Question

State whether the following statement is true or false.Point (-2, -5) is the solution of the linear equation 3x-5y=19:-7x+3y+1=0 .And point (4,9) lies on the linear equation -7x+3y+1=0.

Accepted Answer

Given pair of linear equations:

3x-5y=19  or  3x-5y−19=0     ….
      1

3y-7x+1=0 or  −7x+3y+1=0    ….
      2

Constructing a suitable table with at least two Solutions for each equation in order to produce a graphical representation:From equation (1),

y=
    
     3x−19
    5

Then table for

3x−5y−19=0
   is,We get,

0,−3.8
   
  ,

6.33,0
   
   and

−2,−5
   
  . AndFrom equation (2),

y=
    
     7x−1
    3

Then table for

−7x+3y+1=0
   is,We get,

1,2
   
  ,

0,−0.33
   
   and

4,9
   
  .Then,Create a graph of both equations using the same scale of representation and the same graph paper: We get the graph for the given equations by drawing points

0,−3.8
   
  ,

6.33,0
   
  ,

−2,−5
   
  ,

1,2
   
  ,

0,−0.33
   
   and

4,9
   
   on graph paper and connecting them with lines.In the graph, we observed that these two lines intersect at point (- 2, - 5). ⇒ we get the graphical representation of the given equation. Hence, (- 2, - 5) is the solution of the given equations and yes, point (4, 9) lies on the equation -7x+3y+1=0.Therefore, given statement is true.Hence, option (1) is correct.

State whether the following statement is true or false.

Point (-2, -5) is the solution of the linear equation $3 x - 5 y = 19 : - 7 x + 3 y + 1 = 0$ .

And point (4,9) lies on the linear equation $- 7 x + 3 y + 1 = 0$ .

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