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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