Q. 9 E3.7( 3 Votes )

# Solve graphically the following system of linear equations if it has unique solution:2x — y = 95x + 2y = 27

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. a1 x + b1y + c1 = 0 and a2 x + b2y + c2 = 0, we get

a1 = 2, b1 = – 1 and c1 = – 9

and a2 = 5, b2 = 2 and c2 = – 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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