Question

Solve the system of equations graphically:
2x – 3y + 13 = 0,
3x – 2y + 12 = 0

Answer 1

From the first equation, write y in terms of x

y = `(2x + 13)/3 `          …….(i)
Substitute different values of x in (i) to get different values of y
For x = -5, y = `(-10 + 13 )/3 =1`

For x = 1, y = `(2+13)/3 = 5`

For x = 4, y = ` (8+13)/3 = 7`

Thus, the table for the first equation (2x - 3y + 13 = 0) is

x	-5	1	4
y	1	5	7

Now, plot the points A (-5, 1), B (1, 5) and C (4, 7) on a graph paper and join A, B and C to get the graph of 2x - 3y + 13 = 0.
From the second equation, write y in terms of x

y = `(3x-12)/2 `     …….(ii)
Now, substitute different values of x in (ii) to get different values of y
For x = -4, y = `(-12+12)/2 = 0`

For x = -2, y = `(-6+12)/2= 3`

For x = 0, y = `(0+12)/2= 6`

So, the table for the second equation (3x – 2y + 12 = 0) is

x	-4	-2	0
y	0	3	6

Now, plot the points D (-4, 0), E (-2, 3) and F (0, 6) on the same graph paper and join D, E and F to get the graph of 3x – 2y + 12 = 0.

From the graph, it is clear that, the given lines intersect at (-2, 3).
Hence, the solution of the given system of equation is (-2, 3).