Question 181570
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Multiply the first equation by 4, then multiply the second equation by 3.  That will make the coefficients on <i>y</i> in the two equations additive inverses.


Next, add the two equations term by term to eliminate (hence the name of the method) the <i>y</i> variable, leaving you a single equation in <i>x</i> that can be solved by ordinary algebraic means.


Once you have determined the value of <i>x</i>, substitute that value into either of the original equations and then solve the resulting single-variable equation in <i>y</i>.


The <i>x</i> and <i>y</i> values determined above will give you the coordinates of the ordered pair that represents the single element of the solution set to the system of equations.


Note:  In the event that the elimination process results in a trivial identity, i.e. 0 = 0, then you have a system of two equations that represent the same straight line in *[tex \Large R^2] meaning that you have infinite solutions to the system.  In the event that the elimination process results in an absurdity, such as 0 = 3, then you have the representation of two parallel lines and the solution set for the system is empty.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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