Solve the following pair of linear equations: 152x - 378y = -74

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Q) Solve the following pair of linear equations:

152x – 378y = – 74
– 378 x + 152y = – 604

Ans:

Given the equations:

Solve the following pair of linear equations:
152 x – 378 y = – 74 ….. (i)
– 378 x + 152 y = – 604 ….. (ii)

We need to first simplify the coefficients of variables x and y:

Step 1: Let’s add equation (i) and equation (ii) and we get:

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

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

$\therefore - 226 x - 226 y = - 678$

$\therefore x + y = \frac{- 678}{- 226}$

$\therefore x + y = 3$ ……. (iii)

Step 2: Let’s subtract equation (ii) from equation (i) and we get:

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

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

$\therefore 530 x - 530 y = - 530$

$\therefore x - y = \frac{- 530}{- 530}$

$\therefore x - y = 1$ ……. (iv)

Step 3: Let’s add the equations (iii) and (iv) and we get:

$(x + y) + ( x - y) = (3) + (1)$

$\therefore 2 x = 4$

$\therefore x = 2$

Step 4: Let’s substitute x = 1, in equation (iii), we get:

$(2) + y = 3$

$\therefore y = 3 - 2$

$\therefore y = 1$

Therefore, $x = 2~and~y = 1$

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