`2x - 3y = -2, -4x + 9y = 7` Solve the system of linear equations and check any solutions algebraically.

Friday, October 16, 2009

You may use the reduction method to solve the system, hence, you may multiply the first equation by 2, such that:

$\displaystyle{2}{\left({2}{x}-{3}{y}\right)}={2}\cdot{\left(-{2}\right)}$

$\displaystyle{4}{x}-{6}{y}=-{4}$

You may now add the equation $\displaystyle{4}{x}-{6}{y}=-{4}$ to the equation - $\displaystyle{4}{x}+{9}{y}={7},$ such that:

$\displaystyle{4}{x}-{6}{y}-{4}{x}+{9}{y}=-{4}+{7}$

$\displaystyle{3}{y}={3}\Rightarrow{y}={1}$

You may replace 1 for y in equation $\displaystyle{2}{x}-{3}{y}=-{2}$ , such that:

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

Hence, evaluating the solution to the given system, yields $\displaystyle{x}=\frac{{1}}{{2}},{y}={1}.$

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