Question

Solve the following system of equations graphically:
Shade the region between the lines and the y-axis

4x − y = 4
3x + 2y = 14

Answer 1

 The equations are:

4x − y = 4  ....(i)

3x + 2y = 14  ........(2)

Putting x = 0 in equation (1) we get:

`=> 4 xx 0 - y = 4`

`=> y = -4`

x = 0, y = -4

Putting y = 0 in equation (1) we get

=> 4x - 0 = 4

=> x = 1

x = 1, y = 0

Use the following table to draw the graph:

x	0	1
y	-4	0

Draw the graph by plotting the two points A(0, -4) and B(1,0) from table.

3x + 2y = 14 .....(2)

Putting x = 0 ineqaution (2) we get

`=> 3 xx 0 + 2y = 14`

=> y = 7

x = 0, y = 7

Putting y = 0 in eqaution (2) we get

`=>  3x + 20 xx 0 = 14`

`=> x = 14/3`

x = 14/3, y = 0

Use the following table to draw the graph.

x	0	14/3
y	7	0

Draw the graph by plotting the two points C(0, 7), D(14/3, 0) from table.

Two lines intersect at points P(2,4) of y−axis.

Hence x = 2 and y = 4 is the solution.