Many ways problem

## Problem

Each column and row has a property which some equation or inequality may or may not have. If an example has the properties of the corresponding row and column, then it can appear in that cell.

We have omitted some headings, and some entries in cells. Can you complete the table?

Solutions lie between $1$ and $6$ All values of $x$ are solutions
$x^2 +4 =0$ $5x - 3 = 9-x$
Inequalities $8 -x < 2 - 3x$
$y = 3x$ and $\frac{y}{3} - 1 = x$ $y = 3x+5$ and $y = -x-3$
• Did you have any choice about the row and column headings?

• Can you simplify any of your examples?

• Do all your examples require some ‘solving’ to check they fit the attributes of the cell? If not, can you make it so that they all do?

• If we required all the cells to contain quadratics, would it still be possible to fill all the cells?