Question 316342
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The second equation is already in standard form.  Put the first one in standard form also:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5x\ +\ 2y\ =\ -13]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ -\ 5y\ =\ 7]


Multiply the first equation by 4 and the second one by 5:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -20x\ +\ 8y\ =\ -52]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20x\ -\ 25y\ =\ 35]


Add like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0x\ -\ 17y\ =\ -17]


Solve for *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -17y\ =\ -17]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 1]


Substitute this value for *[tex \LARGE y] in either of the original equations and then solve for *[tex \LARGE x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ -\ 5(1)\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ =\ 12]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 3]


The solution set is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(3,1\right)]


Verify:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2(1)\ =\ 5(3)\ -\ 13]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\ =\ 15\ -\ 13]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4(3)\ -\ 5(1)\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12\ -\ 5\ =\ 7]


The ordered pair we claimed as the solution set satisfies both equations.


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