Question

Solve for x and y:
152x - 378y = -74, -378x + 152y = -604.​

Answer 1

Answer

Given equations,

$\sf 152x - 378y = -74 \: --- (i)$

$\sf - 378 + 152y = -604 \: --- (ii)$

The coefficients of x and y in one equation are interchanged in each other.

Adding (i) and (ii), we get

$\sf \dashrightarrow {152 + (-378)} x + {(-378) + 152} y = -(74 + 604)$

$\sf \dashrightarrow (-226) x + (-226) y = -678$

$\sf \dashrightarrow (-226)(x + y) = -678$

$\sf \dashrightarrow (x + y) = \dfrac{-678}{-226}$

$\sf \dashrightarrow x + y = 3 \: --- (iii)$

Subtracting (ii) from (i),

$\sf \dashrightarrow (152 + 378) x + (-378 - 152) y = (-74 + 604)$

$\sf \dashrightarrow 530x - 530y = 530$

$\sf \dashrightarrow 530 (x - y) = 530$

$\sf \dashrightarrow x - y = 1 \: --- (iv)$

Adding (iii) and (iv), we get

$\sf \dashrightarrow 2x = 4$

Shifting 2 from LHS to RHS.

$\sf \dashrightarrow x = 2$

Subtracting (iv) from (iii), we get

$\sf \dashrightarrow 2y = 2$

Shifting 2 from LHS to RHS,

$\sf \dashrightarrow y = 1$

Thus, x = 2 and y = 1.