10x+y=7(x+y) and 10x+y-36=10y+x | Simultaneous Equations | SciPiPupil

Question: Solve the following pair of simultaneous equation: $10x+y=7(x+y)$ and $10x+y-36 = 10y+x$.

Solution:

Given,

Equation (i) is $10x + y = 7(x +y)$

$or, 10x + y = 7x +7y$

$or, 10x -7x = 7y -y$

$or, 3x = 6y$

$or, 3×x = 3×2×y$

$or, x = 3y$

Equation (ii) is $10x +y-36 = 10y +x$

$or, 10x -x -36 = 10y - y$

$or, 9x = 36 + 9y$

$or, 9×x = 9×(4+y)$

$or, x = 4+y$

Put value of x from equation (i) in equation (ii), we get,

$or, 3y = 4+y$

$or, 3y-y = 4$

$or, 2y = 4$

$or, 2×y = 2×2$

$\therefore y = 2$

Now,

Put value of y in equation (i), we get,

$or, x = 3×2$

$\therefore x = 6$

Hence, (x,y) = (6,2).