Simultaneous Equations (AQA GCSE Further Maths): Exam Questions

Solve the simultaneous equations

$\begin{array}{rcl}2a+b–c& =& 8\\ 4a–3b–2c& =& –9\\ 6a+3b+c& =& 0\end{array}$

         $a=$................, $b=$................, $c=$................  

Solve the simultaneous equations.

$\begin{array}{rcl}4a–b+3c& =& 27\\ 3a+2b–c& =& 5\\ 2a–5c& =& –7\end{array}$

Do not use trial and improvement.

You must show your working.

$a=.................,b=.................,c=.................$

Solve the simultaneous equations

$xy=2$ and $y=3x+5$

Do not use trial and improvement.

You must show your working.

Solve the simultaneous equations

$\begin{array}{rcl}2x-y+3& =& 0\\ x^2-3xy+y^2& =& 11\end{array}$

Do not use trial and improvement.

You must show your working.

Find, to 2 decimal places, the coordinates of the two points of intersection between the line $y=x+1$ and the curve $y=x^2$.

Do not use trial and improvement.

You must show your working.

Two bags of apples plus one bag of carrots cost £9 more than two bags of bananas.

One bag of apples plus two bags of bananas plus two bags of carrots cost £12.

Two bags of apples plus one bag of bananas cost £3 more than two bags of carrots.

By forming and solving simultaneous equations, work out the individual costs of a bag of apples, a bag of bananas and a bag of carrots.

Do not use trial and improvement.

You must show your working.

Solve the simultaneous equations

$\begin{array}{rcl}y-x& =& 2\\ \frac{1}{x}+\frac{1}{y}& =& 1\end{array}$

giving your answers in an exact form.

Do not use trial and improvement.

You must show your working.

$x^2+y^2-4x-4y+7=0$ is the equation of a circle.

$3y-4x=3$ is the equation of a straight line.

Use algebra to show that the straight line is a tangent to the circle at a point, $P$, whose coordinates you should find.