Question

Solve the following systems of equations graphically:

2x + y − 3 = 0

2x − 3y − 7 = 0

Answer 1

The given equations are

=> 2x + y = 3 ......(i)

=> 2x - 3y = 7 ....(ii)

Putting x = 0 in equation (1) we get

`=> 2 xx 0 + y = 3`

`=> y = 3`

x = 0 , y = 3

Piutting y = 0 in equation (1) we get

=> 2x + 0 = 3

=> x = 3/2

x = 3/2,   y = 0

Use the following table to draw the graph. 

x	0	3/2
y	3	0

Draw the graph by plotting the two points A(0,3) and B(3/2, 0) from table

Graph of the equation (2)

2x - 3y = 7

Putting x = 0 in equation (2) we get

`=> 2 xx 0 - 3y = 7`

`=> y = -7/3`

x = 0, y = -7/3

Putting y = 0 in equation (2) we get

`=> 2x - 3x xx 0 = 7`

=> x = 7/2

x = 7/2,  y = 0

Use the following table to draw the graph.

x	0	7/2
y	-7/3	0

Draw the graph by plotting the two points C(0, -7/2)  and D(7/2,0 )from table.

The two lines intersect at points P(2,1).

Hence x = 2, y = -1 is the solution.