Question

Question 7 (v)
Solve the following pair of linear equations.
152x - 378y = - 74
- 378x + 152y = - 604

Answer 1

152x - 378y = - 74
76x - 189y = -37
$x=\frac{189y-37}{76}$ .....(1)
- 378x + 152y = - 604
- 189x + 76y = - 302 ..… (2)
Substituting the value of x in equation (2), we obtain
$-189\left(\frac{189y-37}{76}\right)+76y=-302$
$-(189{)}^{2}y+189\times 37+(76{)}^{2}y=-302\times 76$
$189\times 37+302\times 76=(189{)}^{2}y-(76{)}^{2}y$
$6993+22952=(189-76)(189+76)y$
$29945=\left(113\right)\left(265\right)y$
$y=1$
From equation (1), we obtain
$x=\frac{189\left(1\right)-37}{76}$
$x=\frac{189-37}{76}=\frac{152}{76}$
$x=2$