This video is a fairly popular example of solving simultaneous equations, by substitution, in circles and straight lines. The question asks you to calculate the intersects (where the perimeter and straight line cross each other):
Find the coordinates of the points where line y + 5 = 3x intersects the circle x² + y² = 65.
The easiest way of solving simultaneous equations by substitution is to rearrange y + 5 = 3x to make y the subject … y = 3x – 5, and then substitute back into the circle equation. After a small amount of manipulation, this produces a quadratic equation that is easily solved by factorising. Once you have the x values, you can calculate y, again by substitution.
Download a copy of the questions here: QT – Solving by substitution
Download a copy of the written answers here: QT – Solving by substitution ANSWERS
These types of questions appear in all the main examination boards, including Edexcel, AQA and OCR. They are popular and, once you have the basic principles, fairly similar. Please do stop the video, try the question and compare your solution!
I hope it becomes a little clearer as you work through the quick test videos, before moving on to the higher levels. They do take a bit of a leap forward, although should be OK if you have viewed the earlier ones.
If you would like to find out more try these!
Please do leave a comment below if you are not sure. Alternately you can view my YouTube channel and leave a comment there – I'll always try to respond as quickly as possible.