Simultaneous Equations (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

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

$\begin{array}{rcl}x& =& 7-3y\\ x^2-y^2& =& 39\end{array}$

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

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

$\begin{array}{l}2x+3y=-12\\ 5x+2y=14\end{array}$  

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

Solve the simultaneous equations       $\begin{array}{l}{x}^2+y^2=9\\ x+y=2\end{array}$

Give your answers correct to 2 decimal places.

Solve the equations

$x^2+y^2=36$

$x=2y+6$

The diagram above represents a courtyard with a length of $y$ metres and a width of $10$ metres.

Mark is designing a rectangular path from one side to another, with a width of $x$metres.

The total area of the courtyard, excluding the path, is $116.30{\mathrm{m}}^2$.

A wall is built around the courtyard, along both longer sides and both shorter sides except where the path cuts through. The total length of the wall is $45.52$ metres.

Set up and solve a pair of simultaneous equations to find the value of $x$ and the value of $y$.

Leave your answers to 2 decimal places.

The straight line $y=3x-1$ intersects the curve $y=x^2+x-5$ at the points $P$ and $Q$.

Find the coordinates of $P$ and $Q$.
Give your answers correct to 2 decimal places.

$P$ ( .................... , .................... )

$Q$ ( .................... , .................... )

The straight line $y=2x+1$ intersects the curve $y=x^2+3x–4$ at the points A and B.

Find the coordinates of A and B.
Give your answers correct to 2 decimal places.

A ( .................... , .................... )
B ( .................... , .................... )

The straight line $y=3x+2$ intersects the curve $y=2x^2+7x-11$ at two points.
Find the coordinates of these two points.
Give your answers correct to 2 decimal places.

   (....................... , .......................) 

(....................... , .......................) 

The graphs of $y={\left(x-1\right)}^2$ and $y=\frac{1}{2}x+1$ intersect at A and B.   Find the length of AB.  

AB = ................................................

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

$\begin{array}{rcl}y& =& 4-x\\ x^2+2y^2& =& 67\end{array}$  

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

Marco is making patterns with grey and white circular mats.

The patterns form a sequence. Marco makes a table to show some information about the patterns.

Marco needs a total of 6 mats to make the first pattern.
He needs a total of 16 mats to make the first two patterns.
He needs a total of $\frac{1}{6}{n}^3+a{n}^2+bn$ mats to make the first $n$ patterns.

Find the value of $a$ and the value of $b$.

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