Question

25x +22y =152000.... (i) and 22x + 25y = 153500 ...(ii) simultaneous equation

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equation is

$\rm \: 25x + 22y = 152000 - - - - (i)$

and

$\rm \: 22x + 25y = 153500 - - - - (ii)$

Since, diagonally coefficients are same, so to solve such type of equations, we first add two equations and then subtract second equation from first equation, to get pair of simultaneous linear equations in simplest form.

So, on adding equation (i) and (ii), we get

$\rm \: 47x + 47y = 305500$

$\rm \: 47(x + y) = 305500$

$\rm \: x + y = \dfrac{305500}{47}$

$\rm\implies \:x + y = 6500 - - - (iii)$

Now, on Subtracting equation (ii) from equation (i), we get

$\rm \: 3x - 3y = - 1500$

$\rm \: 3(x - y) = - 1500$

$\rm\implies \:x - y = - 500 - - - - (iv)$

Now, on adding equation (iii) and (iv), we get

$\rm \: 2x = 6000$

$\rm\implies \:x = 3000$

On substituting the value of x in equation (i), we get

$\rm \: 3000 + y = 6500$

$\rm \: y = 6500 - 3000$

$\rm\implies \:y = 3500$

Hence,

$\begin{gathered}\begin{gathered}\bf\: Solution \: is \: \begin{cases} &\sf{x = 3000} \\ \\ &\sf{y = 3500} \end{cases}\end{gathered}\end{gathered}$

Verification

Consider equation (i)

$\rm \: 25x + 22y = 152000$

On substituting the values of x and y, we get

$\rm \: 25(3000) + 22(3500) = 152000$

$\rm \: 75000 + 77000 = 152000$

$\rm \: 152000 = 152000$

Hence, Verified