Blog: `(1/5)x + (1/2)y = 8, x + y = 20` Solve the system by the method of substitution.

Tuesday, October 6, 2009

Express $\displaystyle{y}$ from the second equation: $\displaystyle{y}={20}-{x}.$ Then substitute it into the first equation:

$\displaystyle{\left(\frac{{1}}{{5}}\right)}{x}+{\left(\frac{{1}}{{2}}\right)}{\left({20}-{x}\right)}={8},$ or

$\displaystyle{\left(\frac{{1}}{{5}}\right)}{x}-{\left(\frac{{1}}{{2}}\right)}{x}+{10}={8},$ or

$\displaystyle-{\left(\frac{{3}}{{10}}\right)}{x}=-{2},$ or

$\displaystyle{x}={2}\cdot\frac{{10}}{{3}}=\frac{{20}}{{3}}={6}\frac{{2}}{{3}}.$

Therefore $\displaystyle{y}={20}-{x}={13}\frac{{1}}{{3}}.$

The answer: x=6 and 2/3, y=13 and 1/3.

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