Simultaneous Equations (Cambridge International IGCSE Maths): Exam Questions

Solve the simultaneous equations.

You must show all your working.

$\frac{1}{2}x-3y=9\,5x+y=28$

Solve the simultaneous equations

$\begin{gathered} 2 x + 7 y & = 17 \\ 5 x + 3 y & = - 1 \end{gathered}$

Show clear algebraic working.

$\begin{gathered} x & = .................................. \\ y & = .................................. \end{gathered}$

Solve the simultaneous equations

$\begin{gathered} 5 a + 2 c & = 10 \\ 2 a - 4 c & = 7 \end{gathered}$

Show clear algebraic working.

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

Solve the simultaneous equations

$\begin{gathered} 7 x - 2 y & = 34 \\ 3 x + 5 y & = - 3 \end{gathered}$

Show clear algebraic working.

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

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

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

$2x+3y=-12\,5x+2y=14$

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

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

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

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

Solve the simultaneous equations

$x^{2}+y^{2}=9\,x+y=2$

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.

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

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

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 $\frac{1}{6}n^{3}+an^{2}+bn$ 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 ( .................... , .................... )