Respuesta :
[tex]\begin{gathered} \text{System 1} \\ 2x-y=-11\text{ (1)} \\ -x+3y=\text{ -7 (2)} \\ \text{Solving x from (2)} \\ x=3y+7,\text{ } \\ U\sin g\text{ x in (1)} \\ 2(3y+7)-y=-11 \\ 6y+14-y=-11 \\ 6y-y=-11-14 \\ 5y=-25 \\ y=\frac{-25}{5} \\ y=-5 \\ \text{Hence} \\ x=3(-5)+7 \\ x=-15+7 \\ x=-8 \\ \text{The solution is x=-8 and y=-5} \\ \\ \text{System 2} \\ -x-3y=-4\text{ (1)} \\ 2x+7y=12\text{ (2)} \\ Solv\text{ing x from (1)} \\ x=-3y+4 \\ U\sin g\text{ x in (2)} \\ 2(-3y+4)+7y=12 \\ -6y+8+7y=12 \\ -6y+7y=12-8 \\ y=4 \\ \text{Hence} \\ x=-3(4)+4 \\ x=-12+4 \\ x=-8 \\ \text{The solution is x=}-\text{8 and y=4} \\ \\ \text{System 3} \\ 6x+7y=19\text{ (1)} \\ 5x+2y=-11\text{ (2)} \\ \text{Solving y from (1)} \\ 6x+7y=19 \\ 6x=19-7y \\ x=\frac{19}{6}-\frac{7y}{6} \\ U\sin g\text{ x in (2)} \\ 5(\frac{19}{6}-\frac{7y}{6})+2y=-11\text{ } \\ \frac{95}{6}-\frac{35y}{6}+2y=-11 \\ -\frac{35y}{6}+2y=-11-\frac{95}{6} \\ -\frac{23y}{6}=-\frac{161}{6} \\ y=(-\frac{161}{6})(-\frac{6}{23}) \\ y=7 \\ Hence \\ x=\frac{19}{6}-\frac{7(7)}{6} \\ x=\frac{19}{6}-\frac{49}{6} \\ x=-5 \\ \text{The solution is x=}-5\text{ and y=}7 \\ \\ \text{System 4} \\ -9x-4y=-19\text{ (1)} \\ 3x+2y=11\text{ (2)} \\ Solv\text{ing x from (2)} \\ 3x+2y=11 \\ 3x=11-2y \\ x=\frac{11}{3}-\frac{2y}{3} \\ U\sin g\text{ x in (1)} \\ -9(\frac{11}{3}-\frac{2y}{3})-4y=-19 \\ -33+6y-4y=-19 \\ 6y-4y=-19+33 \\ 2y=14 \\ y=\frac{14}{2} \\ y=7 \\ \text{Hence} \\ x=\frac{11}{3}-\frac{2(7)}{3} \\ x=\frac{11}{3}-\frac{14}{3} \\ x=-1 \\ \text{The solution is x=}-1\text{ and y=}7 \end{gathered}[/tex]
