 # Algebra - Simultaneous Equations - Solving by Any Method

a - answer    s - solution    v - video

## Question 1

Solve the following simultaneous equations

a) \begin{align}y&=x+2\\y&=2x+1\end{align}a s v
b) \begin{align}x+y&=5\\x-y&=1\end{align}a s v
c) \begin{align}x&=2y+8\\x&=3y+2\end{align}a s v
d) \begin{align}x-3y&=2\\x+3y&=8\end{align}a s v
e) \begin{align}x-2y&=3\\x-3y&=0\end{align}a s v
f) \begin{align}2y-x&=8\\6y-x&=28\end{align}a s v

## Question 2

Solve the following simultaneous equations

a) \begin{align}3x+2y&=23\\7x+4y&=51\end{align}a s v
b) \begin{align}2y&=6x+4\\y&=5x-4\end{align}a s v
c) \begin{align}10y-30&=2x\\4y+2x&=54\end{align}a s v
d) \begin{align}3x-5y&=8\\2y+5x&=34\end{align}a s v
e) \begin{align}3x&=38-y\\3y&=16-x\end{align}a s v
f) \begin{align}7x-3y&=55\\4y&=50-2x\end{align}a s v

## Question 3

Solve the following simultaneous equations

a) \begin{align}y-2x&=9\\5y&=23-2x\end{align}a s v
b) \begin{align}3y&=4x+3\\2y&=x-2\end{align}a s v
c) \begin{align}7y&=1+3x\\y+6x&=-32\end{align}a s v
d) \begin{align}5x-6y&=1\\10x+y&=-11\end{align}a s v
e) \begin{align}2x-3y&=-1\\3x+2y&=-21\end{align}a s v
f) \begin{align}4x+7y&=55\\x&=-16-2y\end{align}a s v

## Question 4

Solve the following simultaneous equations. Leave answers as improper fractions where necessary.

a) \begin{align}6x&=y+1\\6y&=24x\end{align}a s v
b) \begin{align}6x-5y&=1\\9x+10y&=5\end{align}a s v
c) \begin{align}12x&=15y+3\\x-y&=\frac{7}{20}\end{align}a s v
d) \begin{align}3y&=2x+3\\4y&=5x-1\end{align}a s v
e) \begin{align}5x-2y&=6\\3y&=8x+15\end{align}a s v
f) \begin{align}3x+10y&=18\\10y-3x&=0\end{align}a s v