Solve the following pair of linear equations by substitution method:
\( x+y=5 \) and \( 2 x-3 y=4 \)
Given:
Given pair of equations is:
\( x+y=5 \) and \( 2 x-3 y=4 \)
To do:
We have to solve the given pair of equations by substitution method.
Solution:
$x+y=5$
This implies,
$x=5-y$.....(i)
$2x-3y=4$
$2(5-y)-3y=4$ [From (i)]
$2(5)-2(y)-3y=4$
$10-2y-3y=4$
$10-4=5y$
$5y=6$
$y=\frac{6}{5}$
Therefore,
$x=5-\frac{6}{5}$
$x=\frac{5\times5-6}{5}$
$x=\frac{25-6}{5}$
$x=\frac{19}{5}$
The values of $x$ and $y$ are $\frac{19}{5}$ and $\frac{6}{5}$ respectively.
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