To solve the system of linear equations 8 x + 5 y = 18 and 6 x + y = negative 2. by using the linear combination method, Amos decided that he should first multiply the second equation by –5 and then add the two equations together to eliminate the y-terms. His calculations are as shown.
8 x + 5 y = 18. + 6 x minus 5 y = 10. 14 x = 28. StartFraction 14 x Over 14 EndFraction = StartFraction 28 Over 14 EndFraction. X = 2.
6 x + y = negative 2. 6 (2) + y = negative 2. 12 + y = negative 2. 12 + y minus 12 = negative 2 minus 12. y = negative 14.
Amos’s solution is (2, –14). What did he do wrong?