Solve the following pair of linear equations by the substitution method.
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
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Solution
0.2x + 0.3y = 1.3 (1)
0.4x + 0.5y = 2.3 (2)
From equation (1), we obtain
x = `(1.3 - 0.3y)/3`
Substituting this value in equation (2), we obtain
`0.4((1.3 - 0.3y)/0.2)+0.5y = 2.3`
2.6 - 0.6y + 0.5y = 2.3
2.6 - 2.3 = 0.1y
0.3 = 0.1y
y = 3 (4)
Substituting this value in equation (3), we obtain
x = `(1.3 - 0.3 xx 3)/0.2`
= `(1.3 - 0.9)/0.2 = (0.4)/(0.2) = 2`
∴ x = 2, y = 3
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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