Find the solution of the pair of equations x – 3y = 5 and 2x + y = 3 ?

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(0,4)

(-2,3)

(-8,4)

(2,-1)

answer is A.

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Detailed Solution

The given equations are

x – 3y = 5 … (1)

2x + y = 3 … (2)

A table can be drawn for the corresponding values of x and y for the equation x – 3y = 5 as

x	$y = \frac{x - 5}{3}$
–1	–2
5	0

The points (–1, –2) and (5, 0) can be plotted on a graph and joined with a straight line to obtain the graph of the equation x – 3y = 5.

Similarly, a table can be drawn for the corresponding values of x and y for the equation 2x + y = 3 as

x	y = (3 – 2x)
0	3
1	1

The points (0, 3) and (1, 1) can be plotted on a graph and joined with a straight line to obtain the graph of the equation 2x + y = 3.

This can be done as

Question Image

The point of intersection of the two lines is the solution of the pair of equations. From the graph, it can be observed that the two lines intersect at the point (2, –1). Therefore, the solution of the given pair of equations is x = 2 and y = –1.

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