# Test: Simultaneous Equations - Ambitious

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Question 1:   Solve: $\left\{\begin{array}{l}\frac{1}{2}x-2y=3\\ -\frac{1}{2}x+3y=5\end{array}$
$\left\{\begin{array}{l}x=38\\ y=8\end{array}$
$\left\{\begin{array}{l}x=24\\ y=4\end{array}$
$\left\{\begin{array}{l}x=32\\ y=12\end{array}$
$\left\{\begin{array}{l}x=19\\ y=6\end{array}$
Question 2:   Solve: $\left\{\begin{array}{l}\frac{1}{3}x+\frac{1}{4}y=\frac{1}{5}\\ \frac{1}{3}x-\frac{3}{4}y=-\frac{1}{5}\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{10}\\ y=\frac{3}{10}\end{array}$
$\left\{\begin{array}{l}x=\frac{3}{10}\\ y=\frac{2}{5}\end{array}$
$\left\{\begin{array}{l}x=1\\ y=2\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{3}\\ y=\frac{2}{3}\end{array}$
Question 3:   Solve: $\left\{\begin{array}{l}2x+3y=13\\ 3x-5y=-9\end{array}$
$\left\{\begin{array}{l}x=2\\ y=3\end{array}$
$\left\{\begin{array}{l}x=5\\ y=6\end{array}$
$\left\{\begin{array}{l}x=1\\ y=2\end{array}$
$\left\{\begin{array}{l}x=2\\ y=5\end{array}$
Question 4:   Solve: $\left\{\begin{array}{l}y=2x+3\\ y=-3x+5\end{array}$
$\left\{\begin{array}{l}x=\frac{2}{5}\\ y=\frac{19}{5}\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-2\end{array}$
$\left\{\begin{array}{l}x=\frac{3}{7}\\ y=5\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{3}\\ y=4\end{array}$
Question 5:   Solve: $\left\{\begin{array}{l}\frac{1}{2}x+\frac{1}{4}y+\frac{1}{5}=0\\ 3\left(x+y\right)-2\left(x-\frac{1}{6}y\right)+5=0\end{array}$
$\left\{\begin{array}{l}x=\frac{7}{17}\\ y=-1\frac{53}{85}\end{array}$
$\left\{\begin{array}{l}x=\frac{3}{7}\\ y=-2\end{array}$
$\left\{\begin{array}{l}x=\frac{2}{15}\\ y=-1\frac{17}{18}\end{array}$
$\left\{\begin{array}{l}x=\frac{7}{19}\\ y=-1\frac{1}{2}\end{array}$
Question 6:   Solve: $\left\{\begin{array}{l}2\left(x+y\right)+3\left(x-5\right)+1=0\\ 3\left(x+y\right)-7\left(y+3\right)=3\end{array}$
$\left\{\begin{array}{l}x=4\\ y=-3\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-2\end{array}$
$\left\{\begin{array}{l}x=5\\ y=2\end{array}$
$\left\{\begin{array}{l}x=2\\ y=-2\end{array}$
Question 7:   Solve: $\left\{\begin{array}{l}\frac{5}{3\left(x-y\right)}+\frac{3}{4\left(2+y\right)}=38\\ \frac{2}{x+5}+\frac{1}{2\left(y+3\right)}=14\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{4}\\ y=1\end{array}$
$\left\{\begin{array}{l}x=1\\ y=-1\end{array}$
$\left\{\begin{array}{l}x=2\\ y=1\end{array}$
$\left\{\begin{array}{l}x=\frac{2}{5}\\ y=\frac{1}{3}\end{array}$
Question 8:   Solve: $\left\{\begin{array}{l}x+y+z=6\\ 2x-y+3z=9\\ x+2y-3z=-4\end{array}$
$\left\{\begin{array}{l}x=-1\\ y=2\\ z=3\end{array}$
$\left\{\begin{array}{l}x=2\\ y=-1\\ z=4\end{array}$
$\left\{\begin{array}{l}x=1\\ y=2\\ z=3\end{array}$
$\left\{\begin{array}{l}x=3\\ y=-2\\ z=-5\end{array}$
Question 9:   Solve: $\left\{\begin{array}{l}2x+y=0\\ 3x-2y+\frac{3}{5}=2\end{array}$
$\left\{\begin{array}{l}x=\frac{2}{5}\\ x=\frac{3}{5}\end{array}$
$\left\{\begin{array}{l}x=1\\ x=-2\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{5}\\ y=-\frac{2}{5}\end{array}$
$\left\{\begin{array}{l}x=\frac{1}{3}\\ y=-\frac{4}{5}\end{array}$
Question 10:   Solve: $\left\{\begin{array}{l}\frac{x+2}{4}-3y=9\\ x-\frac{\left(x+3y\right)}{-4}=11\end{array}$
$\left\{\begin{array}{l}x=12\\ y=-5\end{array}$
$\left\{\begin{array}{l}x=10\\ y=-2\end{array}$
$\left\{\begin{array}{l}x=9\\ y=-1\end{array}$
$\left\{\begin{array}{l}x=11\\ y=-4\end{array}$