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Q.

The system of linear equations 4x – y = 4, 3x + 2y = 14 is solved graphically. What is the solution of the given pair of equations?


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a

x = 2 and y = 4

b

x = 1 and y = 4

c

x = 2 and y = 1

d

x = 0 and y = 2  

answer is A.

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Detailed Solution

Given pair of linear equations, 4x−y=4;3x+2y=14  .
We have to find the solution of the equation.
4x − y = 4                        ……(1)
From equation 1, we get, y=4x−4   and the table for 4x−y−4=0   is,
Question ImageSo, the points are 0,−4  , 1,0   and 2,4  .
From equation 2,
3x+2y=14 ⇒2y=14−3x ⇒y= 14−3x 2  
Then table for 3x + 2y − 14=0   is,
Question ImageSo, the points are 0, 7 , 14 3 =4.67,0  and  2, 4    .
On plotting points 0,−4 , 1,0 and 2,4 .   and 0, 7 , 14 3 =4.67,0  and  2, 4     on the graph paper and joining them by a line, we get the following graph for the above equations.
Question ImageIn the graph, we observed that these two lines intersect at point C (2, 4).
Hence, x = 2 and y = 4 is the solution of the given pair of equations.
Hence, option 1 is correct.
 
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