### Intersections

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

### Negatively Triangular

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

### Which Is Cheaper?

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

# Which Is Bigger?

##### Stage: 4 Challenge Level:

Mike, James, Toby, Molly and Harry from Highfields School, Owen, Estee and Emma from Montessori School, Connor from Gladesmore School, and Karnan from Stag Lane Junior all came up with a similar explanation for the first part of the problem.

Jasmine from Highfields explained:

I plotted both equations on a graph. From this I found out that they both intercept when x=7 Therefore from the graph I have found that:
When n=7,both equations are the same value
When n< 7, n+10 is the biggest
When n> 7, 2n+3 is the biggest
Charlie and Alison got different answers because one person chose a value below 7 and one person chose a value above 7. This method works with every set of equations where you have to find the biggest.

Zak explained how a graph helped:
From looking at this graph we can see that the line with the equation 2n+3 has a larger gradient and so overtakes the line with the equation n+10 even though it starts off lower, so because 2n+3 has a larger gradient it will be larger after n=7.