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Q.

The system of linear equations x-y=1, 2x + y=8 is solved graphically. What is the solution of the given pair of equations?


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a

x = 1 and y = 2

b

x = 3 and y = 2

c

x = 2 and y = 3

d

x = 3 and y = 0  

answer is B.

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Detailed Solution

Given pair of linear equations is,
x− y=1                            ……(1)
2x+y=8                          ……(2)
From (1),
x−y=1 ⇒y=x−1  
For a table for (1):
Question ImageSo, the points are 1,0 , 0,−1 and 3,2 .  
From equation 2,
2x+y=8 ⇒y=8−2x  
The table for 2x+y−8=0   is,  Question ImageSo, the points are 4,0 , 0,8 and 3,2  .
On plotting the points 1,0 , 0,−1  and 3,2   and 4,0 , 0,8   and 3,2   on the graph paper. The graph for the aforementioned equations is obtained by connecting them with a line.
Question ImageIn the graph, we observed that these two lines intersect at point (3, 2).
Hence, x = 3 and y = 2 is the solution of the given pair of equations.
Thus, option 2 is correct.
 
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