## 6.4 Systems with a Single Parameter

### System of Equations with a Single Parameter

- We have seen how simultaneous equations look like. For instance,

\left\{\begin{array}{ll}6=x+y+z & (1) \\ 4=4 x+2 y+z & (2)\end{array}\right.

and how there can be unique, infinite or no solutions for each set of simultaneous equations. These are explored in section “Solving Simultaneous Linear Equations” in A2 – Algebra.

- Literal equations are very similar, just that instead of just numbers, we will have unknown constants. Such as,

\left\{\begin{array}{ll}x+y=2 m+3 & (1) \\ 3 x-2 y=7 m-1 & (2)\end{array}\right.

where m is a constant. Hence the solution (x,\ y) will be expressed in terms of m, and again there are unique, infinite, or no solutions. This will depend on the value(s) of m.

- Parameters are a little different from literals. They are technically speaking, variables and not constants. It can be seen as a link between two (or more) variables.
- For instance, take a cuboid with side length x for example. We denote the surface area as S, volume as V, then we have