Solve the following pair of linear …

The given pair of linear equations
8x + 5y = 9 ...(1) ...(1)
3x + 2y = 4 ...(2) ...(2)

1. by substituting method
   From equation (2), 2y = 4 - 3x
   {tex}\Rightarrow \;y = \frac{{4 - 3x}}{2}{/tex} ...(3)
   Substitute this value of y in equation (1), we get
   {tex}8x + 5\left( {\frac{{4 - 3x}}{2}} \right) = 9{/tex}
   {tex}\Rightarrow{/tex} 16x + 20 - 15x = 18
   {tex}\Rightarrow{/tex} x + 20 = 18
   {tex}\Rightarrow{/tex} x = 18 - 20
   {tex}\Rightarrow{/tex} x = -2
   substituting this value of x in equation (3), we get
   {tex}y = \frac{{4 - 3( - 2)}}{2} = \frac{{4 + 6}}{2} = \frac{{10}}{2} = 5{/tex}
   So the solution of the given pair of linear equations is x = -2, y = 5.
2. by cross-multiplication method
   Let us write the given pair of linear equation is
   8x + 5y - 9 = 0 ...(1)
   3x + 2y - 4 = 0 ...(2)
   To solve the equation (1) and (2) by cross multiplication method,
   we draw the diagram below:
   
   Then,
   {tex}\frac{x}{{(5)( - 4) - (2)( - 9)}} = \frac{y}{{( - 9)(3) - ( - 4)(8)}}{/tex}{tex} = \frac{1}{{(8)(2) - (3)(5)}}{/tex}
   {tex}= \frac{x}{{ - 20 + 18}} = \frac{y}{{ - 27 + 32}} = \frac{1}{{16 - 15}}{/tex}
   {tex}\Rightarrow \frac{x}{{ - 2}} = \frac{y}{5} = \frac{1}{1}{/tex}
   {tex}\Rightarrow{/tex} x = -2 and y = 5
   Hence, the required solution of the given pair of linear equations is x = -2, y = 5.
   Verification : substituting x = -2, y = 5, we find that both the equation (1) and (2) are satisfied as shown below:
   8x + 5y = 8(-2) + 5(5) = -16 + 25 = 9
   3x + 2y = 3(-2) + 2(5) =- 6 + 10 = 4
   Hence, the solution is correct.