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Algebra, Functions, Graphs, and Vectors 39

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
2
1
1
2
the variableð are represented by x and y. The substitution
method of solving these equationð consistð in performing either
of the following sequenceð of steps. If a 0, use Sequence A.
1
If a 0, use Sequence B. (If botà a 0 and a 0, the set
2
1
1
of equationð is in fact a pair of equationð in termð of a single
variable, and the following stepð are irrelevantÑ
Sequence A: First, solve the first equation for x in termð of y:
ax bð c 0
1
1
1
ax bð c 1
1
1
x ( bð c )/a 1
1
1
Next, substitute the above-derived solution for x in place of x in
the second equation, obtaining:
a ( bð c )/a bð c 0
1
1
2
2
1
2
Solve this single-variable equation for y, using the previously
outlined ruleð for solving single-variable equations. Assuming
a solution exists, it can be substituted for y in either of the
original equations, deriving a single-variable equation in termð
of x. Solve for x, using the previously outlined ruleð for solving
single-variable equations.
Sequence B: Because a 0, the first equation has only one
1
variable, and is in the following form:

bð c 0
1
1
Solve this equation for y:

bð c 1
1

y c /b 1
1
This can be substituted for y in the second equation, obtaining: