Question

Solve the following system of equations graphically:

2x + y = 6, 2x – y – 2 = 0. Find the area of the triangle so formed by two lines and x-axis.

Answer 1

Our equations are

2x + y = 6 ....(1)

2x – y – 2 = 0 

2x – y = 2  ......(2)

For Equation (1)

2x + y = 6

Putting x = 0

2(0) + y = 6

0 + y = 6

y = 6

So, x = 0, y = 6 is a solution, i.e., (0, 6) is a solution.

Putting y = 0

2x + 0 = 6

x = `6/3`

x = 3

So, x = 3, y = 0 is a solution, i.e., (3, 0) is a solution.

x	0	3
y	6	0

For Equation (2)

2x – y = 2

Putting x = 0

2(0) – y = 2

0 – y = 2

–y = 2

y = –2

So, x = 0, y = –2 is a solution i.e., (0, 2) is a solution.

Putting y = 0

2x – 0 = 2

x = `2/2`

x = 1

So, x = 1, y = 0 is a solution, i.e., (1, 0) is a solution.

x	0	1
y	–2	0

We will plot both equations on the graph:

Area of Required triangle:

Triangle has Base = 2 units and Height = 2 units

Thus, Area of triangle = `1/2` × Base × Height

= `1/2` × 2 × 2

= 2 square units