Question

Solve the following pair of linear (simultaneous) equation by the method of elimination by substitution:

0.2x + 0.1y = 25

2(x - 2) - 1.6y = 116

Answer 1

The given pair of linear equations are

0.2x + 0.1y = 25                      ...(1)

2(x - 2) - 1.6y = 116                ...(2)

Consider equation (1)

0.2x + 0.1y = 25

⇒ `(0.2x)/10+(0.1y)/10=25`

⇒ `(2x+y)/10=25`

⇒ 2x + y = 250

⇒ y = 250 - 2x              ...(3)

Putting the value of y in equation (2)

⇒ 2(x - 2) - 1.6(250 - 2x) = 116

⇒ 2x - 4 - 400 + 3.2x = 116

⇒ 5.2x - 404 = 116

⇒ 5.2x = 116 + 404

⇒ 5.2x = 520

⇒ x = `520/5.2`

⇒ x = 100

From equation in (3)

`0.2/10(100) + 0.1y = 25`

`20+y/10=25`

`y/10=25-20`

`y/10=5`

y = 50