Problem
ALG-B1-M03-P015 A System with Product of Differences
#15
★★★☆☆ Level 3 of 5
Solve the system \(x+y=5\), \(x^2-y^2=15\).
Factor \(x^2-y^2\).
\(x^2-y^2=(x-y)(x+y)\). Since \(x+y=5\), we get \(5(x-y)=15\), so \(x-y=3\).
Solving \(x+y=5\), \(x-y=3\), gives \(x=4\), \(y=1\).
Shows how one equation unlocks the other.