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

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

$$\begin{gathered} y=5x^2+4x-19 \\ y=4x+1 \end{gathered}$$

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

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

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

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

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

Solve algebraically the simultaneous equations

$$\begin{gathered} x^2+y^2=25 \\ y-2x=5 \end{gathered}$$

In this question, all measurements are in centimetres.

The height of the triangle is $h-3$ and the height of the rectangle is $h$.

The length of the base of the triangle and rectangle are both $x$.

Write down an expression for the area of the triangle.

The area of the triangle is $15{\mathrm{cm}}^2$ and the area of the rectangle is $42{\mathrm{cm}}^2$.

Show that $x=4$

Find the value of $h$.

The diagram shows a curve with equation $y=2x^2-2x-7$.
The straight line with equation $y=3x+5$ intersects the curve at the points A and B.

Find the coordinates of the points A and B.

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

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.

Solve these simultaneous equations algebraically.

$y=2x^2-7x+4$

$y=4x-1$

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