Solve the following simultaneous equations
$0.5 x + 0.6 y = 2.3$
$0.2 x + 0.7 y = 2.3$

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Solution

The given equations are
$0.5 x + 0.6 y = 2.3$ ......(i)
$0.2 x + 0.7 y = 2.3$ .....(ii)
Multiplying equation (i), by $2$ and (ii) by $5$
$x + 1.2 y = 4.6$
$x + 3.5 y = 11.5$
and then subtracting, we get
$- 2.3 y = - 6.9$
$\Rightarrow y = 3$
Putting $y = 3$ in (i), we get
$0.5 x + 0.6 \times 3 = 2.3$
$\Rightarrow 0.5 x + 1.8 = 2.3$
$\Rightarrow 0.5 x = 2.3 - 1.8$
$\Rightarrow 0.5 x = 0.5$
$\Rightarrow x = 1$
Hence the required solution is $x = 1, y = 3.$

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