x+y=5 and 10x+y-9=10y+x | Simultaneous Equations | SciPiPupil

Question: Solve the following pair of simultaneous equation: $x+y=5$ and $10x +y-9=10y+x$

Solution:

Given,

Equation (i) is $x + y=5$

$or, x = 5-y$

Equation (ii) is $10x +y -9 = 10y +x$

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

$10(5-y) + y -9 = 10y +(5-y)$

$or, 50 - 10y + y -9 = 10y + 5 - y$

$or, 41 - 9y = 9y +5$

$or, 41-5 = 9y +9y$

$or, 36 = 18y$

$or, 18×2 = 18×y$

$or, 2 = y$

$\therefore y = 2$

And,

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

$or, x = 5 - 2$

$\therefore x = 3$

Hence, (x,y) = (3,2).

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