Question

Solve the following systems of equations graphically:

2x + 3y + 5 = 0

3x − 2y − 12 = 0

Answer 1

The given equations are

2x + 3y + 5 = 0 ....(i)

3x -2y - 12 = 0 ...(ii)

Putting x = 0 in equation (i) we get

`=> 2 xx 0 + 3y = -5`

=> y = -5/3

x = 0 ,  y = -5/3

Putting y = 0 in equation (i) we get

`=> 2x + 3 xx 0 = -5`

`=> x = -5/2`

`x = -5/2, y = 0`

Use the following table to draw the graph.

x	0	-5/2
y	-5/3	0

Draw the graph by plotting the two points from table.

Graph of the equation ...(ii)

3x - 2y = 12 ...(ii)

Putting x = 0 in equation (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 from table.

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

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