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Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

The student is given the equations of a line and a circle, and has to find the coordinates of the points of intersection. They're always at integer coordinates.

Solving a system of simultaneous congruences using the Chinese Remainder Theorem.

An explore mode question which allows you to write a solution straight away, or break it down into steps.

After solving a system of three congruences, you can ask for a new problem with more congruences.

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Straightforward solving linear equations question

A simultaneous equations question with integers only

Straightforward solving linear equations question

Straightforward solving linear equations question

A simultaneous equations question with integers only

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

Students need to find solution to simultaneous linear equations with randomised coefficients.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Simultaneous equation problem as circuit analysis to find unknown voltages. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.
They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solving a pair of simultaneous equations of the form $y=mx+c_1$ and $y=ax^2+kx+c_2$ to find the possible values for the unknown coefficient $k$, when given the values of $m$, $a$, $c_1$ and $c_2$.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.