Question

Solve the following systems of equations graphically:
x + y = 4

2x − 3y = 3

Answer 1

The given equations are

x + y = 4   ...(i)

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

Putting x = 0 in equation (i) we get

=> o + y = 4

=> y = 4

`:. x = 0, y = 4`

Use the following table to draw the graph.

x	0	4
y	4	0

Draw the graph by plotting the two points  A(4,0) and B(4,0) from table

Graph of the equation (ii)

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

Putting x = 0 in equation (ii) we get

`=>  0 - 3y = 3`

`=> y = -1`

`:. x = 0, y = -1`

Putting y = 0 in equation (ii) 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	-1	0

Draw the graph by plotting the two points C(0,-1) and D(3/2, 0) from table

The two lines intersect at points P(3,1)

Hence x = 3, y = 1 is solution