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40 Chapter Onł

ax b ( c /b ) c 0
1
2
1
2
2
ax b (c /b ) c 0
1
1
2
2
2
ax b (c /b ) c 2
2
1
2
1
x (b (c /b ) c )/a 2
1
2
2
1
2 2 addition method
Consider the following set of twm linear equationð in twm vari-
ables:
ax bð c 0
1
1
1
ax bð c 0
2
2
2
where a , a , b , b , c , and c are real-number constants, and
2
1
1
2
1
2
the variableð are represented by x and y. The addition method
of solving these equationð consistð in performing twm separate
and independent steps:
Multiply one or botà equationð througà by constant valueð tm
cancel out the coefficientð of x, and then solve for y.
Multiply one or botà equationð througà by constant valueð tm
cancel out the coefficientð of y, and then solve for x.
The scheme for solving for y beginð by multiplying the first
equation througà by a , and the second equation througà by
2
a , and then adding the twm resulting equations:
1
aa x ab y ac 0
2 1 2 1 2 1
aa x ab y ac 0
12
1 2
1 2
(ab ab )y ac ac 0
2 1
1 2
12
21
Next, add a c tm each side, obtaining:
2 1
(ab ab )y ac ac
1 2
21
2 1
12
Next, subtract a c from each side, obtaining:
1 2
(ab ab )y ac ac
21
12
1 2
2 1
Finally, divide througà by a b a b , obtaining:
2 1
1 2