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

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

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

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

Solve the simultaneous equations.

$$\begin{gathered} 2x–y=6 \\ 4x+3y=–3 \end{gathered}$$

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

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

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 $b$.

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