Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4

Solution :

The given linear equations are :

8x + 5y = 9              ………..(1)

3x + 2y = 4              ………..(2)

By Substitution Method :

Form equation (1),  y = \(9 – 8x\over 5\)

Substitute the value of y in equation (2), we get

3x + 2(\(9 – 8x\over 5\)) = 4

or   15x + 18 – 16x = 20     \(\implies\)   x = -2

Putting x = – 2 in equation (1), we get

8(-2) + 5y = 9    \(\implies\)   5y = 9 + 16 = 25

\(\implies\)  y = 5

Hence,  x = -2 and y = 5.

By Cross-Multiplication Method :

The given linear equation can be written as :

8x + 5y – 9 = 0

3x + 2y – 4 = 0

So, we have

\(x\over -20 + 18\)  =  \(y\over -27 + 32\)  =  \(1\over 16 – 15\)

\(\implies\)   \(x\over -2\)  =  \(y\over  5\)  =  \(1\over 1\)

\(\implies\)   x = -2  and y = 5

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