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