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

Friday, May 31, 2013

$\displaystyle{3}{x}-{y}={9},{x}-{2}{y}=-{2}$ Solve the system of linear equations and check any solutions algebraically.

$\displaystyle{3}{x}-{y}={9}$

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

From the second equation,

$\displaystyle{x}=-{2}+{2}{y}$

Substitute the above expression of x in the first equation,

$\displaystyle{3}{\left(-{2}+{2}{y}\right)}-{y}={9}$

$\displaystyle-{6}+{6}{y}-{y}={9}$

$\displaystyle-{6}+{5}{y}={9}$

$\displaystyle{5}{y}={9}+{6}$

$\displaystyle{5}{y}={15}$

$\displaystyle{y}=\frac{{15}}{{5}}$

$\displaystyle{y}={3}$

Plug the value of y in the expression,

$\displaystyle{x}=-{2}+{2}{y}$

$\displaystyle{x}=-{2}+{2}\cdot{3}$

$\displaystyle{x}=-{2}+{6}$

$\displaystyle{x}={4}$

Now let's check the solution by plugging in the equations,

Plug in the solutions in the first equation,

$\displaystyle{3}\cdot{4}-{3}={9}$

9=9

Plug in the solution in the second equation,

$\displaystyle{4}-{2}\cdot{3}=-{2}$

$\displaystyle{4}-{6}=-{2}$

$\displaystyle-{2}=-{2}$

Solutions satisfy both the equations

Hence the solutions of the equations are x=4 and y=3

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