Secondary
Problem: find two ticket prices
One child ticket and one adult ticket cost 70 baht. Two child tickets and one adult ticket cost 100 baht. With prices x and y, the equations are x + y = 70 and 2x + y = 100.
Compare the models
Draw one child unit and one adult unit for the first purchase. The second adds one child unit and costs 30 baht more. The extra unit shows the child price is 30 baht.
The lines intersect at (30, 40), satisfying both x + y = 70 and 2x + y = 100.
View larger image ↗Eliminate and substitute
Subtract the first equation from the second: (2x + y) − (x + y) = 100 − 70, giving x = 30. Substitute into x + y = 70 to obtain y = 40. The pair (30, 40) must satisfy both equations.
Connect the graph to the solution
The lines y = 70 − x and y = 100 − 2x intersect at (30, 40), satisfying both conditions. Extend: if the second purchase costs 110 baht while the first stays at 70 baht, the prices become x = 40 and y = 30. Check 40 + 30 = 70 and 80 + 30 = 110.
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