Solutions vs Answers
for David L Ragozin's sections of Math 308, Spring 2004
Find numbers x,y which satisfy the equations:
E_{1} : x + 2y = 1
E_{2} : 2x + 7y = -1
An answer : x = 3 , y = -1.
A professionals solution : Gaussian elimination yields x = 3 , y = -1.
A solution:Subtract 2 * E_{1} from E_{2} to eliminate x, yieldingE_{1} : x + 2y = 1Divide E'_{2} by 3 to solve for y:
E'_{2} : 3y = -3E_{1} : x + 2y = 1Subtract 2 * E''_{2} from E_{1} to eliminate y, yielding the solution
E''_{2} : y = -1E_{1} : x = 3
E'''_{2} : y = -1
Note that the answer provides no reasons, explanations. Although a reader who knows something about equations may be able to check the answer.