Question

Solve the system of equations graphically:

2x + 3y + 5 = 0, 3x – 2y – 12 = 0

Solve the following system of equations graphically:

2x + 3y + 5 = 0, 3x – 2y – 12 = 0

Answer 1

From the first equation, write y in terms of x

`y = -((5 + 2x)/3)`   ...(i)

Substitute different values of x in (i) to get different values of y

For x = –1, y = `-(5 - 2)/3 = -1`

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

For x = 5, y = `-(8 + 10)/3 = -5`

Thus, the table for the first equation (2x + 3y + 5 = 0) is

x	–1	2	5
y	–1	–3	–5

Now, plot the points A(–1, –1), B(2, –3) and C(5, –5) on a graph paper and join them to get the graph of 2x + 3y + 5 = 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 = 0, y = `(0 - 12)/2 = -6`

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

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

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

x	0	2	4
y	–6	–3	0

Now, plot the points D(0, –6), E(2, –3) and F(4, 0) 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).