Q. 9 E3.7( 3 Votes )

# Solve graphically the following system of linear equations if it has unique solution:

2x — y = 9

5x + 2y = 27

Answer :

The given pair of linear equations is

2x – y = 9 or 2x – y – 9 = 0

and 5x + 2y = 27 or 5x + 2y – 27 = 0

On comparing the given equations with standard form of pair of linear equations i.e. a_{1} x + b_{1}y + c_{1} = 0 and a_{2} x + b_{2}y + c_{2} = 0, we get

a_{1} = 2, b_{1} = – 1 and c_{1} = – 9

and a_{2 =} 5, b_{2} = 2 and c_{2} = – 27

The lines representing the given pair of linear equations will intersect at a point.

Now, table for or

Now, table for or

Here, the lines intersecting at point C i.e. (5,1)

Hence, the unique solution is x = 5 and y = 1.

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