$$\DeclareMathOperator{cosec}{cosec}$$

# Number and Algebra

Syllabus Content

Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinite number of solutions or no solution.

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## Furthermore

Official Guidance, clarification and syllabus links:

These systems should be solved using both algebraic and technological methods, for example row reduction or matrices.

Systems which have no solution(s) are inconsistent.

Finding a general solution for a system with an infinite number of solutions.

The augmented matrix can be used to determine the number of solutions:

$$\left[\begin{array}{ccc|c}a & b & c & d\\0 & e & f & g\\0 & 0 & h & i\end{array}\right]$$

If $$h \neq 0$$ there is a unique solution.

If $$h = 0 \text{ and } i \neq 0$$ there is no solution

If $$h = 0 \text{ and } i = 0$$ there are infinitely many solutions (let $$z=t$$).

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