Draw the graph of the equation 2x + 3y = –5 and x + y = –1 in the same graph. Find the co-ordinates of the point of intersection of the two lines.

Solution

2x + 3y = -5
$rightwards double arrow$ 3y = - 5 - 2x
$rightwards double arrow$ $straight y space equals fraction numerator negative 5 minus 2 straight x over denominator 3 end fraction$

Table of solutions

X	–1	2
y	–1	–3

We plot the points (–1, –1) and (1, –3) on a graph paper and join the same by a ruler to get the line which is the graph of the equation 2x + 3y = –5.

x + y = –1

⇒ y = – 1 – x

Table of solutions

X	0	1
y	–1	–2

We plot the points (0, –1) and (1, –2) on the same graph paper and join the same by a ruler to get the line which is the graph of the equation x + y = –1.
From graph, we see that the coordinates of the point of intersection of the two lines are (2, –3).