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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
Solution
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
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