Question

Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y-axis.

Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis. Calculate the area of the triangle so formed.

Answer 1

The given equations are: 

5x − y = 5 ........(i)

3x − y = 3 ...........(ii)

Putting x = 0 in equation (i) we get

`=> 5 xx 0 - y = 5`

`=> y = -5`

x = 0, y = -5

Putting y = 0 in eqaution (i) we get

`=> 5x - 0 = 5`

`=> x = 1`

x = 1, y = 0

Use the following table to draw the graph.

x	0	1
y	-5	0

Draw the graph by plotting the two points A(0, -5), B(1, 0) from table

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

Putting x = 0 in eqaution (ii) we get

`=> 3xx0-y = 3`

`=> y = -3`

`x= 0, y = -3`

Putting y = 0 in equation (ii) we get

`=> 3x - 0 = 3`

`=> x = 1`

x = 1, y = 0

Use the following table to draw the graph.

x	0	1
y	-3	0

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

Hence the vertices of the required triangle are B(1,0), C(0, -3) and A(0, -5).

Now,

Required area = Area of PCA.

Required area = `1/2 ("base" × "height")`.

Required area = `1/2 (2 xx 1)` sq.units.

Hence the required area is 1 sq units.