Y=6x-11 -3x-2y=7 solve by substitution

Friday, October 5, 2007

Y=6x-11 -3x-2y=7 solve by substitution

When simplifying equations that are done simultaneously it is important to make one variable the subject of the formula to simplify solving the equations.

We already have y the subject of the formula of the one equation:

$\displaystyle{y}={6}{x}-{11}$

Now we can make y the subject of the formula for the next equation:

$\displaystyle-{3}{x}-{2}{y}={7}$

$\displaystyle-{3}{x}-{7}={2}{y}$ (apply inverse operations)

$\displaystyle\frac{{-{3}{x}-{7}}}{{2}}={y}$ (apply inverse operations)

Since we have two equations, we can now equate the two equations and solve for x:

$\displaystyle{6}{x}-{11}=\frac{{-{3}{x}-{7}}}{{2}}$

$\displaystyle{2}{\left({6}{x}-{11}\right)}=-{3}{x}-{7}$ (inverse operations)

$\displaystyle{12}{x}-{22}=-{3}{x}-{7}$ (multiply out)

Now get the variable x on the one side, and the constants on the other side:

$\displaystyle{12}{x}+{3}{x}=-{7}+{22}$ (apply inverse operations)

$\displaystyle{15}{x}={15}$

$\displaystyle{x}={1}$

Since we know what x is, we can substitute it in the first equation as it is the easiest equation:

$\displaystyle{y}={6}{\left({1}\right)}-{11}$

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

SUMMARY: $\displaystyle{x}={1},{y}=-{5}$

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Friday, October 5, 2007

Y=6x-11 -3x-2y=7 solve by substitution

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