Solve the following system of equations by using the method of substitution,
$3 x - 5 y = - 1$ and $x - y = - 1$ .

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Solution

The given system of equations is
$3 x - 5 y = - 1$ ..... (i)
$x - y = - 1$ ......(ii)

From (ii), we get
$y = x + 1$

Substituting $y = x + 1$ in (i), we get
$3 x - 5 (x + 1) - 1$
$\Rightarrow - 2 x - 5 = - 1$
$\Rightarrow - 2 x = 4 \Rightarrow x = - 2$

Putting $x = - 2$ in $y = x + 1$ we get $y = - 1$ .

Hence, the solution of the given system of equations is $x = - 2, y = - 1$ .

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