Simultaneous Equations (Cambridge (CIE) IGCSE International 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  

     $$\begin{gathered} x^2+y^2=9 \\ x+y=2 \end{gathered}$$

You must show all your working.

Give your answers correct to 2 decimal places.

Solve the equations

$x^2+y^2=36$
$x=2y+6$

You must show all your working.

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 $b$.

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

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

Use an algebraic method to find the coordinates of A and B.
Give your answers correct to 2 decimal places.

You must show all your working.

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