Question

Solve the following systems of equations graphically:

2x + 3y = 4

x − y + 3 = 0

Answer 1

The given equations are:

2x + 3y = 4     ....(i)

x − y + 3 = 0     ...(ii)

Putting x = 0 in equation (i) we get

`=> 2 xx 0 + 3y = 4`

=> y = 4/3

x = 0, y = 4/3

Putting y = 0 in equation (i) we get

`=> 2x + 3 xx 0 = 4`

=> x = 2

x = 2, y = 0

Use the following table to draw the graph.

x	0	2
y	4/3	0

Draw the graph by plotting the two points  A(0, 4/3) and B(2,0) from table

Graph of the equation   ... (ii)

x - y = -3  ...(ii)

Putting x = 0 in equation (ii) we get

=> 0 - y = -3

=> y = 3

x= 0, y = 3

Putting y = 0 in equation (ii) we get

=> x - 0 = -3

=> x = -3

x= -3, y = 0

Use the following table to draw the graph.

x	0	-3
y	3	0

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

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

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