Question

If
$5x + 4y = 13 \: and \: 4x + 5y = 14 \: find \: x - y$
​

Answer 1

$\red{\large \underline{ \rm{Solution}}}$

$\sf \: 5x + 4y = 13 \quad(1) \\ \sf \: 4x + 5y = 14 \quad(2)$

By Substitution Method

Multiply eq (1) with 5 and eq (2) with 4

$\sf \quad 25x + \cancel{20y} = 65 \quad(1) \\ ( - )\sf \: 16x + \cancel{ 20y} = 56 \quad(2) \\ \sf( - ) \quad( - ) \quad( - )$

$\sf \: 9x = 9 \qquad \: \underline{ \boxed{ \sf \: x = 1}}$

Substitute the value of x in either of two eq let's take eq 2.

$\sf \: 4(1) + 5y = 14 \\ \sf \: 5y = 14 - 4 \\ \sf \: 5y = 10 \qquad \: \underline{\boxed {\sf { y = 2}}}$

To Find

$\sf \: x - y = 1 - 2 = \red{ - 1}$