Blog: `0.5x + 3.2y = 9.0, 0.2x - 1.6y = -3.6` Solve the system by the method of substitution.

Friday, August 28, 2015

Multiply everything by 10 to get whole numbers

Solve equation [2] for the variable x

$\displaystyle{2}{x}={16}{y}-{36}$

$\displaystyle{x}={8}{y}-{18}$

Plug this in for variable x in equation [1]

$\displaystyle{5}{\left({8}{y}-{18}\right)}+{32}{y}={90}$
$\displaystyle{72}{y}={180}$

Solve equation [1] for the variable y

$\displaystyle{72}{y}={180}$

$\displaystyle{y}=\frac{{5}}{{2}}$

By now we know this much :

$\displaystyle{x}={8}{y}-{18}$
$\displaystyle{y}=\frac{{5}}{{2}}$

Use the y value to solve for x

$\displaystyle{x}={8}{\left(\frac{{5}}{{2}}\right)}-{18}={2}$

The solution is $\displaystyle{\left({2},\frac{{5}}{{2}}\right)}$

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