Two Variables, One Line
A pair of equations
Turn a problem with two unknowns into a pair of equations.
One equation in two unknowns has infinitely many solutions. A second condition narrows them down.
Rakesh's puzzle: two numbers with sum 25 and difference 11 give x + y = 25 and x – y = 11. His table of tries found 18 and 7.
A solution of the pair is an ordered pair that satisfies both equations at once.
Exhibition tickets: 2 adults + 3 children = ₹600, and 3 adults + 2 children = ₹700, give 2x + 3y = 600 and 3x + 2y = 700. The real prices must make both bills right.
Taxi fares: a fixed charge x plus y per km. 6 km for ₹122 gives x + 6y = 122.
In general, a pair looks like:
- a1x + b1y + c1 = 0
- a2x + b2y + c2 = 0
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