Question

Solve the following systems of equations graphically:

2x − 3y + 13 = 0

3x − 2y + 12 = 0

Answer 1

The given equations are:

2x − 3y + 13 = 0 ........(i)

3x − 2y + 12 = 0 ......(ii)

Putting x = 0 in equation (i) we get

`=> 2 xx 0 - 3y = -13`

`=> y = 13/3`

x = 0, y = 13/3

Putting y = 0 in equaion (i) we get

`=> 2x - 3 xx 0 = -13`

`=> x = -13/2`

x = -13/2, y = 0

Use the following table to draw the graph.

x	0	-13/2
y	13/3	0

Draw the graph by plotting the two points A(0, 13/2) and B(-13/2, 0) from table

Graph of the equation...(ii)

3x - 2y =  -12 ...(ii)

Putting x = 0 in equaiton (ii) we get

`=> 3 xx 0 - 2y = -12`

=> y = 6

x = 0, y = 6

Putting y = 0 in equation (ii) we get

`=> 3x - 2 xx 0 = -12`

`=> x = -4`

x = -4, y = 0

Use the following table to draw the graph.

x	0	-4
y	6	0

Draw the graph by plotting the two points C(0, 6) and D(-4, 0) from table.

The two lines intersect at points P(-2,3).

Hence, x = -2 and y = 3 is the solution.