Question

Represent the following pair of linear equations graphically and hence
comment on the consistency of this pair: 3x - y = 7, 2x + 5y + 1 = 0​

Answer 1

The representation of the following pair of linear equations graphically is as shown below.

3x - y = 7

⇒ 3x - y - 7 = 0 ..........(1)

2x + 5y + 1 = 0​ ...........(2)

2 (1) - 3 (2) gives,

x = 2

y = -1

Therefore, from the graph, it's clear that they intersect at a point with coordinates (2, -1)

The lines intersect at a point which represents the unique solution of the system of linear equations in two variables.