Question

$55x + 67y = 311$
$67x + 55y = 299$
A --- (2,3)
B --- (3,2)
C --- (-2,3)
D --- (3,-2)

choose from above
​

Answer 1

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

Given pair of linear equation are

$\rm :\longmapsto\:55x + 67x = 311 - - - - (1)$

and

$\rm :\longmapsto\:67x + 55x = 299 - - - - (2)$

To solve such pair of simultaneous equations where diagonally elements are same, we have to first add two equations and then subtract two equations to reduce in to simplest form.

Adding equation (1) and (2), we get

$\rm :\longmapsto\:122x + 122y = 610$

$\rm :\longmapsto\:122(x + y) = 610$

$\bf\implies \:x + y = 5 - - - - (3)$

On Subtracting equation (2) from (1), we get

$\rm :\longmapsto\: - 12x + 12y = 12$

$\rm :\longmapsto\: 12(- x + y) = 12$

$\bf\implies \: - x + y = 1 - - - - (4)$

On adding equation (3) and (4), we get

$\rm :\longmapsto\:2y = 6$

$\rm\implies \:\boxed{\tt{ \: \: y = 3 \: \: }} - - - - (5)$

On substituting the value of y in equation (3), we get

$\rm :\longmapsto\:x + 3 = 5$

$\rm :\longmapsto\:x = 5 - 3$

$\rm\implies \:\boxed{\tt{ \: \: x \: = \: 2 \: \: }}$

Hence,

Solution of pair of linear equations is

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \: \begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 3} \end{cases}\end{gathered}\end{gathered}$

VERIFICATION

$\rm :\longmapsto\:55x + 67x = 311$

On substituting the values of x and y, we get

$\rm :\longmapsto\:55 \times 2 + 67 \times 3 = 311$

$\rm :\longmapsto\:110 + 201 = 311$

$\rm :\longmapsto\:311 = 311$

HENCE, VERIFIED