Question

5x + 4y = 11 2x + 6y = -7

Answer 1

$\left\{\begin{array}{ccc}5x+4y=11&|\cdot2\\2x+6y=-7&|\cdot(-5)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+8y=22\\-10x-30y=35\end{array}\right}\ \ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ \ \ \ \ \ -22y=57\ \ \ \ |:(-22)\\.\ \ \ \ \ \ \ \ \ \ \ y=-\dfrac{57}{22}\\\\substitute\ the\ value\ of\ y\ to\ the\ first\ equation\\\\5x+4\left(-\dfrac{57}{22}\right)=11\\\\5x-2\cdot\dfrac{57}{11}=11\ \ \ \ |\cdot11\\\\55x-114=121\ \ \ \ |+114\\\\55x=135\ \ \ \ |:55$

$x=\dfrac{135}{55}\\\\x=\dfrac{27}{11}\\\\Answer:\ x=\dfrac{27}{11}\ and\ y=-\dfrac{57}{22}\to\left(\dfrac{27}{11},\ -\dfrac{57}{22}\right)$