# Algebra - 3 or More Simultaneous Equations

a - answer    s - solution    v - video    d - discussion

## Question 1

Solve the following

a) \begin{align}x+y+z&=15\\x+y&=7\\x-y&=3\end{align}a s v d

b) \begin{align}a-b-c&=4\\a+b+c&=14\\b-c&=3\end{align}a s v d

c) \begin{align}2p+q+r&=33\\p+q+r&=25\\5q-r&=7\end{align}a s v d

d) \begin{align}5y-x+2z&=45\\2x-5z&=14\\z-5x&=11\end{align}a s v d

## Question 2

Solve the following

a) \begin{align}x+2y-3z&=-10\\x-y+z&=10\\x-y+2z&=18\end{align}a s v d

b) \begin{align}5s-t+3u&=52\\s+t+u&=20\\4s-2t+u&=29\end{align}a s v d

## Question 3

Solve the following

a) \begin{align}x+y+z&=11\\x+y-z&=9\\2x+y-z&=14\end{align}a s v d

b) \begin{align}3a+4b+2c&=39\\5a-b-2c&=6\\4a+10b+2c&=84\end{align}a s v d

c) \begin{align}4x-5y-8z&=-154\\10x+5y+6z&=240\\x-5y-2z&=-61\end{align}a s v d

d) \begin{align}4p-q-r&=50\\r+q-2p&=-20\\5q-3p-r&=-19\end{align}a s v d

## Question 4

Solve the following

a) \begin{align}5x+2y+8z&=77\\3x+y-3z&=7\\4x-4y+z&=29\end{align}a s v d

b) \begin{align}2x+6y-z&=47\\6x-2y+5z&=37\\8x-4y+3z&=13\end{align}a s v d

c) \begin{align}p-3q-5r&=-61\\12q+3p+2r&=46\\6p-5q+8r&=78\end{align}a s v d

d) \begin{align}2a-5b-10c&=-49\\3a+10b+7c&=50\\11a-b+5c&=131\end{align}a s v d

## Question 5

Solve the following

a) \begin{align}x+2y-z&=-8\\3x+3y-2z&=-9\\5x-y+7z&=90\end{align}a s v d

b) \begin{align}2x-3y+5z&=38\\5x+5y+9z&=67\\4x-4y-6z&=-52\end{align}a s v d

## Question 6

Solve the following

a) \begin{align}3a-b+2c-d&=18\\7a+b+3c+2d&=54\\2a+b+8c+6d&=57\\4a-b-3c+d&=7\end{align}a s v d

b) \begin{align}p-2q+4r-s&=-71\\2p-3q+10r-5s&=-161\\3p+5q+2r+s&=56\\5p-q+3r+2s&=-42\end{align}a s v d