Question

Solve the system of equations graphically:

3x + 2y = 12, 5x – 2y = 4

Solve the following 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 - 4)/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).