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=-(57)/(22)\\\\substitute\ the\ value\ of\ y\ to\ the\ first\ equation\\\\5x+4\left(-(57)/(22)\right)=11\\\\5x-2\cdot(57)/(11)=11\ \ \ \ |\cdot11\\\\55x-114=121\ \ \ \ |+114\\\\55x=135\ \ \ \ |:55`

`x=(135)/(55)\\\\x=(27)/(11)\\\\Answer:\ x=(27)/(11)\ and\ y=-(57)/(22)\to\left((27)/(11),\ -(57)/(22)\right)`