Blog: `1.5x + 0.8y = 2.3, 0.3x - 0.2y = 0.1` Solve the system by the method of substitution.

Thursday, February 26, 2009

First multiply everything by 10 to get whole numbers.

Solve equation [2] for the variable x

$\displaystyle{3}{x}={2}{y}+{1}$

$\displaystyle{x}={2}\frac{{y}}{{3}}+\frac{{1}}{{3}}$

Plug this in for variable x in equation [1]

$\displaystyle{15}{\left({2}\frac{{y}}{{3}}+\frac{{1}}{{3}}\right)}+{8}{y}={23}$
$\displaystyle{18}{y}={18}$

Solve equation [1] for the variable y

$\displaystyle{18}{y}={18}$

$\displaystyle{y}={1}$

By now we know this much :

$\displaystyle{x}={2}\frac{{y}}{{3}}+\frac{{1}}{{3}}$
$\displaystyle{y}={1}$

Use the y value to solve for x

$\displaystyle{x}={\left(\frac{{2}}{{3}}\right)}{\left({1}\right)}+\frac{{1}}{{3}}={1}$

The solution is $\displaystyle{\left({1},{1}\right)}$

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