Solve the following pair of linear equations by the substitution method.
$x+y=14$
$x-y=4$
$x+y=14$
$x-y=4$
(A) $x+y=14$ $....(1)$
$x-y=4$ $....(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$x=14-y$ $....(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$(14-y)-y=4$
$14-2y=4$
$14-4=2y$
$10=2y$
$y=5$ $....(4)$
Now,substituting the value of $y=5$ into equation $(3)$:
$x=14-5$
$x=9$
Therefore,the solution is $x=9$ and $y=5$.
$x-y=4$ $....(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$x=14-y$ $....(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$(14-y)-y=4$
$14-2y=4$
$14-4=2y$
$10=2y$
$y=5$ $....(4)$
Now,substituting the value of $y=5$ into equation $(3)$:
$x=14-5$
$x=9$
Therefore,the solution is $x=9$ and $y=5$.
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