Blog: `x^2 + y^2 = 25, 2x + y = 10` Solve the system graphically or algebraically. Explain your choice of method.

Tuesday, July 19, 2011

Let's solve this system algebraically. The reasons are: a) not to draw a graph and b) highest accuracy.

Express $\displaystyle{y}$ from the second equation, $\displaystyle{y}={10}-{2}{x},$ and substitute it into the first equation:

$\displaystyle{{x}}^{{2}}+{{\left({10}-{2}{x}\right)}}^{{2}}={25},$ or

$\displaystyle{{x}}^{{2}}+{100}+{4}{{x}}^{{2}}-{40}{x}={25},$ or

$\displaystyle{5}{{x}}^{{2}}-{40}{x}+{75}={0},$ or

$\displaystyle{{x}}^{{2}}-{8}{x}+{15}={0}.$

It is simple to find the roots among the dividers of 15, there are x=5 and x=3.

The corresponding y's are 0 and 4.

The answer: 1) x=5, y=0; 2) x=3, y=4.

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