Since reversing the digits gives a new number which is 9 more than the
original number, the equation is
ð 10 xþyÞþ 9 ¼ð 10 yþxÞ
IMPLEMENTATION: Solve the system
xþy¼ 15
10 xþyþ 9 ¼ 10 yþx
Solve the first equation fory, substitute in the second equation and
findx.
xþy¼ 15
xxþy¼ 15 x
y¼ 15 x
10 xþyþ 9 ¼ 10 yþx
10 xþð 15 xÞþ 9 ¼ 10 ð 15 xÞþx
10 xþ 15 xþ 9 ¼ 150 10 xþx
9 xþ 24 ¼ 150 9 x
9 xþ 9 xþ 24 ¼ 150 9 xþ 9 x
18 xþ 24 24 ¼ 150 24
18 x¼ 126
181 x
181
¼
126
18
x¼ 7
Findy:
xþy¼ 15
7 þy¼ 15
210 LESSON 18 Using Two Equations