Question

33x + 32y =34, 32x +33y= 31
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Answer 1

Appropriate Question :-

Solve for x and y :- 33x + 32y =34, 32x +33y= 31

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

Given pair of linear equation are

$\rm \: 33x + 32y= 34 - - - (1)$

and

$\rm \: 32x + 33y= 31 - - - (2)$

On adding equation (1) and (2), we get

$\rm \: 65x + 65y = 65$

$\rm \: 65(x + y) = 65$

$\rm\implies \:x + y = 1 - - - (3)$

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

$\rm\implies \:\rm \: x - y = 3 - - - (4)$

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

$\rm \: 2x = 4$

$\rm\implies \:x = 2 - - - (5)$

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

$\rm \: 2 + y = 1$

$\rm \: y = 1 - 2$

$\rm\implies \:y \: = \: - \: 1 - - - (6)$

Hence,

$\rm\implies \:\boxed{\rm{  \:x = 2 \: }} \: \: \: \: and \: \: \: \: \boxed{\rm{  \:y \: = \: - \: 1 \: }}$

$\rule{190pt}{2pt}$

Verification :-

Consider first equation

$\rm \: 33x + 32y= 34$

On substituting the values of x and y, we get

$\rm \: 33(2) + 32( - 1)= 34$

$\rm \: 66 - 32= 34$

$\rm \: 34 = 34$

Hence, Verified

Consider second equation

$\rm \: 32x + 33y= 31$

On substituting the values of x and y, we get

$\rm \: 32(2) + 33( - 1)= 31$

$\rm \: 64 - 33= 31$

$\rm \: 31= 31$

Hence, Verified