Q. 9 F5.0( 2 Votes )

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

3y = 5 — x

2x = y + 3

Answer :

The given pair of linear equations is


x + 3y = 5 or x + 3y – 5 = 0


and 2x – y = 3 or 2x – y – 3 = 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 = 1, b1 = 3 and c1 = – 5


and a2 = 2, b2 = – 1 and c2 = – 3




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. (2,1)


Hence, the unique solution is x = 2 and y = 1.


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