Solve the following system of equations by the method of substitution:
$3 a - 2 b = 12$ , $4 a - 5 b = 16$

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Solution

Given equations are
$3 a - 2 b = 12$ ....(1)
and $4 a - 5 b = 16$ ....(2)
Therefore, $3 a = 12 + 2 b \Rightarrow a = \frac{12 + 2 b}{3}$ .....(3)
Substitute this value of $a$ in equation (2), we get
$4 (\frac{12 + 2 b}{3}) - 5 b = 16$
$\Rightarrow 48 + 8 b - 15 b = 48$
$\Rightarrow b = 0$
Put this value of $b$ in equation (3)
$\Rightarrow a = \frac{12}{3}$
$\Rightarrow a = 4$
Therefore, the solution is $a = 4, b = 0$ .

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