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. 

Simultaneous equations with at least one non-linear equation

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 $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ 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.

Questions for practising algebraic methods for solving linear simultaneous equations

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

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

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

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

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.

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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

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.

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.