How to do simultaneous equations?
- Give the student an example question.e.g: past paper question from OCR (higher tier) paper 4 2017
Each week Dan drives two routes, route x and route y.
One week he drives route x three times and route y twice.He drives a total of 134 miles that week.
Another week he drives route x twice and route y five times.He drives a total of 203 miles that week.
Find the length of each route.
Answer:i) Turn the question into equations:3X + 2Y = 134 .... eq(a)2X + 5Y = 203 .... eq(b)
ii) method one: Make one term identicalmultiply eq(b) by 1.53X + 7.5Y = 304.5 take away from this eq(a)5.5Y = 170.5divide by 5.5Y = 31Place Y=31 back into eq(a) or eq(b) to find X3X + 2(31) = 1343X = 134 -62 = 72X=24
ii) Method 2: substitutionMake X the subject in eq(b)divide by 2X + 2.5Y = 101.5X = 101.5 - 2.5YSubstitute into eq(a)3( 101.5 - 2.5Y) + 2Y = 134304.5 - 7.5 Y + 3Y = 134304.5 - 5.5Y = 134170.5 = 5.5YDivide by 5.5Y=31like before substitute this value of Y into eq(a) or eq(b) to find X = 24
