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Age 14 to 16 ShortChallenge Level

What is the area of the triangle formed by the three lines whose equations are given below?$$y-x=6\qquad x-2y=3\qquad x+y=6$$

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.