Question

Solve the system of equations graphically:
3x + 2y = 12,
5x – 2y = 4

Answer 1

The given equations are:
3x + 2y = 12 …..(i)

5x – 2y = 4      …..(ii)
From (i), write y in terms of x
y = `(12 − 3x)/2`          …..(iii)
Now, substitute different values of x in (iii) to get different values of y
For x = 0, y = `(12- 3x)/2 = (12-0)/2 = 6`

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

For x = 4, y = ` (12 - 3x )/2 = (12 - 12)/2 = 0`

Thus, the table for the first equation (3x + 2y = 12) is

x	0	2	4
y	6	3	0

Now, plot the points A (0, 6), B(2, 3) and C(4, 0) on a graph paper and join
A, B and C to get the graph of 3x + 2y = 12.
From (ii), write y in terms of x

y`= (5x - 4)/2`               ….(iv)

Now, substitute different values of x in (iv) to get different values of y
For x = 0, y ` = ( 5x - 4)/2 = (0-4)/2 = -2`

For x = 2, y = `(5x - a)/2 = (10- 4)/2 = 3`

For x = 4, y = ` (5x - 4)/2 = (20-4)/2 = 8`

Thus, the table for the first equation (5x – 2y = 4) is

x	0	2	4
y	-2	3	8

Now, plot the points D (0, -2), E (2, 3) and F (4, 8) on the same graph paper and join D, E and F to get the graph of 5x – 2y = 4.

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