Question 1

1. 2x-y=-11-x+3y=-72. 6x+7y=195x+2y=-113. -9x-4y=-193x+2y=11

Question 2

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

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