Blog: `-x + 3y = 17, 4x + 3y = 7` Use any method to solve the system.

Saturday, April 6, 2013

$\displaystyle-{x}+{3}{y}={17},{4}{x}+{3}{y}={7}$ Use any method to solve the system.

EQ1: $\displaystyle-{x}+{3}{y}={17}$

EQ2: $\displaystyle{4}{x}+{3}{y}={7}$

To solve this system of equation, let's apply substitution method. To do so, isolate the x in the first equation.

$\displaystyle-{x}+{3}{y}={17}$

$\displaystyle-{x}={17}-{3}{y}$

$\displaystyle{x}=\frac{{{17}-{3}{y}}}{{-{1}}}$

$\displaystyle{x}=-{17}+{3}{y}$

Then, plug-in this to the second equation.

$\displaystyle{4}{x}+{3}{y}={7}$

$\displaystyle{4}{\left(-{17}+{3}{y}\right)}+{3}{y}={7}$

And, solve for y.

$\displaystyle-{68}+{15}{y}={7}$

$\displaystyle{15}{y}={7}+{68}$

$\displaystyle{15}{y}={75}$

$\displaystyle{y}=\frac{{75}}{{15}}$

$\displaystyle{y}={5}$

Now that the value of y is known, solve for x. Plug-in y = 5 to the first equation.

$\displaystyle-{x}+{3}{y}={17}$

$\displaystyle-{x}+{3}{\left({5}\right)}={17}$

$\displaystyle-{x}+{15}={17}$

$\displaystyle-{x}={17}-{15}$

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

$\displaystyle{x}=\frac{{2}}{{-{1}}}$

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

Therefore,...

EQ1: $\displaystyle-{x}+{3}{y}={17}$

EQ2: $\displaystyle{4}{x}+{3}{y}={7}$

To solve this system of equation, let's apply substitution method. To do so, isolate the x in the first equation.

$\displaystyle-{x}+{3}{y}={17}$

$\displaystyle-{x}={17}-{3}{y}$

$\displaystyle{x}=\frac{{{17}-{3}{y}}}{{-{1}}}$

$\displaystyle{x}=-{17}+{3}{y}$

Then, plug-in this to the second equation.

$\displaystyle{4}{x}+{3}{y}={7}$

$\displaystyle{4}{\left(-{17}+{3}{y}\right)}+{3}{y}={7}$

And, solve for y.

$\displaystyle-{68}+{15}{y}={7}$

$\displaystyle{15}{y}={7}+{68}$

$\displaystyle{15}{y}={75}$

$\displaystyle{y}=\frac{{75}}{{15}}$

$\displaystyle{y}={5}$

Now that the value of y is known, solve for x. Plug-in y = 5 to the first equation.

$\displaystyle-{x}+{3}{y}={17}$

$\displaystyle-{x}+{3}{\left({5}\right)}={17}$

$\displaystyle-{x}+{15}={17}$

$\displaystyle-{x}={17}-{15}$

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

$\displaystyle{x}=\frac{{2}}{{-{1}}}$

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

Therefore, the solution is (-2,5).

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Saturday, April 6, 2013

$\displaystyle-{x}+{3}{y}={17},{4}{x}+{3}{y}={7}$ Use any method to solve the system.

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What is the Exposition, Rising Action, Climax, and Falling Action of "One Thousand Dollars"?

Saturday, April 6, 2013

Use any method to solve the system.

No comments:

Post a Comment

What is the Exposition, Rising Action, Climax, and Falling Action of &quot;One Thousand Dollars&quot;?

$\displaystyle-{x}+{3}{y}={17},{4}{x}+{3}{y}={7}$ Use any method to solve the system.

What is the Exposition, Rising Action, Climax, and Falling Action of "One Thousand Dollars"?