Question

Draw the graphs of the following equations on the same graph paper:

2x + 3y = 12

x – y = 1.

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis.

Answer 1

The given equations are

2x + 3y = 12 ......(i)

x − y = 1 .....(ii)

Putting x = 0 in equation (i) weget

`=> 2 xx 0 + 3y = 12`

`=> y = 4`

x = 0, y = 4

Putting y = 0 in equation (i) we get

`=> x + 3 xx 0 = 6`

`=> x = 6, y = 0`

Use the following table to draw the graph.

x	0	6
y	4	0

Draw the graph by plotting the two points A(0, 2) and B(6, 0) from table

x - y = 1 .....(ii)

Putting x = 0 in equation (ii) we get

`=> 0 - y = 1`

`=> y = -1`

x = 0, y = -1

Putting y = 0 in equation (ii) we get

`=> x - 0 = 1`

`=> x = 1`

x = 1, y = 0

Use the following table to draw the graph.

x	0	1
y	-1	0

Draw the graph by plotting the two points C(0, -1), D(1, 0) from table.

Draw the graph by plotting the two points from the table.

The intersection point is P(3, 2).

Three points of the triangle are A(0, 4), C(0, -1) and P(3, 2).

Hence the value of x = 3 and y = 2.