Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Write and solve a system from two context constraints
Problem
Adult tickets cost \(\$12\) and child tickets cost \(\$8\). Ten tickets cost \(\$104\) total. Let \(a\) and \(c\) be the adult and child ticket counts. Write the system and solve for \(a\) and \(c\).
Big Picture
What this problem is really about
The context provides two independent constraints on two ticket counts. We’ll define each variable with its ticket type, translate the total count and total cost separately, and solve the resulting system while keeping each price attached to the matching count. Both equations and the nonnegative whole-number domain must hold before the counts make sense.
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