Question 192984
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x - 3y = -6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x - 2y = 7]


Multiply the 2nd equation by 4, making the coefficient on x in the 2nd equation  the additive inverse of the coefficient on x in the first equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -4x - 8y = 28]


Add this to the 1st equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x - 4x - 3y - 8y = -6 + 28 \ \ \Rightarrow\ \ \ 0x - 11y = 22]


Notice that the x variable has been eliminated.


Solve for y


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = -2]


Substitute this value for y into either of the original equations; let's use equation 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x - 2(-2) = 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x + 4 = 7]


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


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


The solution set is then *[tex \large \{(-3, -2)\}]


Check:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4(-3) - 3(-2) = -6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -12 + 6 = -6] Checks



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -(-3) - 2(-4) = 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3 + 4 = 7] Checks



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