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Question
Solve the following pair of linear equations by the substitution method.
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
Solution
0.2x + 0.3y = 1.3 ...(1)
0.4x + 0.5y = 2.3 ...(2)
From equation (1), we obtain
y = `(1.3 - 0.2x)/3` ...(3)
Substituting this value in equation (2), we obtain
`0.4((1.3 - 0.2y)/0.3)+0.5y = 2.3`
⇒ `0.4x + [(0.65 - 0.1x)/0.3]= 2.31`
⇒ 0.3 × 0.4x + 0.65 - 0.1x = 0.3 × 2.3
⇒ 0.12x + 0.65 - 0.1x = 0.69
⇒ 0.02x = 0.69 - 0.65 = 0.04
⇒ `x = 0.04/0.02`
⇒ x = 2
Substituting this value in equation x = 2 in (3), we obtain
y = `(1.3 - 0.2 xx 3)/0.3`
y = `(1.3 - 0.4)/0.3`
y = `(0.9)/(0.3)`
y = 3
∴ x = 2, y = 3
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