# Test: Simultaneous Equations - Challenging

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Question 1:   Solve: $\left\{\begin{array}{l}7x+7y=0\\ 2x-5y=1\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{2}\\ y=-\frac{1}{2}\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{5}\\ y=-\frac{1}{5}\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{7}\\ y=-\frac{1}{7}\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-1\end{array}$
Question 2:   Solve: $\left\{\begin{array}{l}-2x-3y-3=0\\ \frac{1}{2}y+2y+7=0\end{array}$
$\left\{\begin{array}{l}x=7\\ y=-4\end{array}$
$\left\{\begin{array}{l}x=4\\ y=5\end{array}$
$\left\{\begin{array}{l}x=6\\ y=-5\end{array}$
$\left\{\begin{array}{l}x=3\\ y=-2\end{array}$
Question 3:   Solve: $\left\{\begin{array}{l}\frac{2x-y}{2}-y=9\\ -2x-y+2=0\end{array}$
$\left\{\begin{array}{l}x=2\\ y=-3\end{array}$
$\left\{\begin{array}{l}x=4\\ y=-4\end{array}$
$\left\{\begin{array}{l}x=3\\ y=-4\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-1\end{array}$
Question 4:   Solve: $\left\{\begin{array}{l}-4x-3y+1=0\\ 2x+2y-\frac{1}{3}=0\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{3}\\ y=-\frac{2}{3}\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{2}\\ y=-\frac{1}{3}\end{array}$ 
$\left\{\begin{array}{l}x=\frac{1}{5}\\ y=-\frac{1}{6}\end{array}$
$\left\{\begin{array}{l}x=2\\ y=-3\end{array}$
Question 5:   Solve: $\left\{\begin{array}{l}x+y=5\\ x\cdot y=6\end{array}$
$\left\{\begin{array}{l}x=-1\\ y=6\end{array}$
$\left\{\begin{array}{l}x=1\\ y=6\end{array}$
$\left\{\begin{array}{l}x=1\\ y=4\end{array}$
$\left\{\begin{array}{l}x=2\\ y=3\end{array}$
Question 6:   Solve: $\left\{\begin{array}{l}x+y=2\\ x\cdot y=3\end{array}$
$\left\{\begin{array}{l}x=-1\\ y=3\end{array}$
$\left\{\begin{array}{l}x=1\\ y=1\end{array}$
$\left\{\begin{array}{l}x=0\\ y=2\end{array}$
Question 7:   Solve: $\left\{\begin{array}{l}x+y-4=0\\ {x}^{2}+{y}^{2}-8=0\end{array}$
$\left\{\begin{array}{l}x=2\\ y=2\end{array}$
$\left\{\begin{array}{l}x=-3\\ y=5\end{array}$
$\left\{\begin{array}{l}x=-2\\ y=4\end{array}$
$\left\{\begin{array}{l}x=1\\ y=3\end{array}$
Question 8:   Solve: $\left\{\begin{array}{l}x\cdot y=-6\\ 2x-\frac{1}{2}xy-2y=-7\end{array}$
$\left\{\begin{array}{l}x=-\frac{1}{2}\\ y=12\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-6\end{array}$
$\left\{\begin{array}{l}x=9\\ y=-\frac{2}{3}\end{array}$
$\left\{\begin{array}{l}x=-2\\ y=3\end{array}$
Question 9:   Solve: $\left\{\begin{array}{l}2x-3y+z=-3\\ -x+\frac{1}{2}y-2z=-8\\ x+y+z=6\end{array}$
$\left\{\begin{array}{l}x=-1\\ y=2\\ z=5\end{array}$
$\left\{\begin{array}{l}x=-1\\ y=-2\\ z=5\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-2\\ z=4\end{array}$
$\left\{\begin{array}{l}x=1\\ y=2\\ z=3\end{array}$
Question 10:   Solve: $\left\{\begin{array}{l}x+y+z=6\\ x-y-z=-4\\ x+y-z=0\end{array}$
$\left\{\begin{array}{l}x=4\\ y=3\\ z=-1\end{array}$
$\left\{\begin{array}{l}x=1\\ y=2\\ z=3\end{array}$
$\left\{\begin{array}{l}x=2\\ y=2\\ z=2\end{array}$
$\left\{\begin{array}{l}x=1\frac{1}{2}\\ y=2\frac{1}{2}\\ z=2\end{array}$