Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x +5y =9 …(1) 3x +2y =4 …(2)

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

8x +5y =9       …(1)

 3x +2y =4      …(2)

 Substitution method :-

8x +5y =9

Subtract 8x both sides we get

5y  = 9 – 8x

Divide by 5

Y = (9 – 8 x)/5 …(3)

Plug this value of y in equation second we get

3x +2y =4

3x  + 2(9 – 8 x)/5) = 4

Multiply by 5 we get

15 x  + 18  - 16 x  = 20

-x  = 2

X = - 2

Plug this value back in equation (3) we get 

Y = (9- 8(-2))/5

Y = 25/5

Y = 5

Answer is x  = -2 and y = 5

Cross multiplication method

8x +5y =9       …(1)

Subtract 9 both side we get

8x +5y – 9 = 0

 3x +2y =4      …(2)

Subtract 4 both side we get

3x + 2y – 4 = 0

Compare with

            we get 

a1 = 8 ,           b1 = 5  ,         and     c1 = -9 

a2  = 3 ,          b2  = 2            and     c2 = -4

Use the formula of cross multiplication

We get

X  = -2   and y = 5