Solve the following system of equations by the method of substitution:
$7 x + 5 y = 10$ , $3 x + y = 2$

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Solution

Given equations are $7 x + 5 y = 10$ ....(1)
and $3 x + y = 2$ ....(2)
Therefore, $y = 2 - 3 x$ ....(3)
Substitute this value of $y$ in equation (1), we get
$7 x + 5 (2 - 3 x) = 10$
$\Rightarrow 7 x + 10 - 15 x = 10$
$\Rightarrow - 8 x = 0$
$\Rightarrow x = 0$
Put this value $x$ in equation (3),
$y = 2 - 0$
$\Rightarrow y = 2$
Therefore, solution is $x = 0, y = 2$ .

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