Simultaneous Equations (Cambridge (CIE) O Level Maths): Exam Questions

Solve the simultaneous equations. You must show all your working.  

$\begin{array}{rcl}6x+5y& =& 27\\ 5x-3y& =& 44\end{array}$  

$x=$..................................................
 $y=$..................................................

Solve the simultaneous equations.
You must show all your working.

$\begin{array}{rcl}2x+\frac{1}{2}y& =& 13\\ 3x+2y& =& 17\end{array}$

$x$ = ............................................ 
$y$ = ............................................ 

These are the first four diagrams of a sequence. The diagrams are made from white dots and black dots.

$T$is the total number of dots used to make all of the first  $n$ diagrams.

$T=a{n}^3+b{n}^2$ 

Find the value of $a$ and the value of $b$.
You must show all your working.

$a=$ ................................................

$b=$................................................ 

There are only $r$ red counters and $g$ green counters in a bag.

A counter is taken at random from the bag.

The probability that the counter is green is $\frac{3}{7}$

The counter is put back in the bag.

$2$ more red counters and $3$ more green counters are put in the bag.
A counter is taken at random from the bag.
The probability that the counter is green is $\frac{6}{13}$

Find the number of red counters and the number of green counters that were in the bag originally.

$x:y=7:4$

$x+y=88$

Work out the value of $x–y$

The prices of two phones are in the ratio x : y.

When the prices are both increased by £20, the ratio becomes 5 : 2.
When the prices are both reduced by £5, the ratio becomes 5 : 1.

Express the ratio x : y in its lowest terms.