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197
M
odel
3: A
pplying
the
S
olution
to
the
P
roblem
The solution to a solved equation can be tested by substituting each solution into the equation and
making sure that the solution makes the equation correct. Note: This is only part of the validation; if
you didn’t come up with all of the solutions, this process won’t inform you that you have missed one
or more of the solutions in the solution set.
2
2
2 3 5 9
2( 2) 3( 2) 5 9
2(4) 6 5 9
8 6 5 9
9 9
x x
− − =
− − − − =
+ − =
+ − =
=
Validate that one of the solutions to the equation
2
2 3 5 9
x x
− − =
is
x
= –2
by substituting this value for
x
in the equation:
M
odel
4: U
nit
A
nalysis
When solving a word problem that involves units, it is possible to check your result by ensuring that
the units match. Errors can occur when converting one type of unit to another. This method is also
called
dimensional analysis
.
For example, if converting 231 cm to yards, we might have the following computation.
1
1
231
12
364
2.54
3
yd
≈
Using unit analysis, we have
231
cm
1
2.54
in
cm
2
2
12 1
364
3
in yd
in yd
ft
ft
ft
≈
The dimensions (units) are not correct. The correct result would be:
231
cm
1
in
2.54
cm
1
ft
12
in
1
3
yd
ft
2.53
yd
≈
M
odel
5: U
se
a
S
econd
P
rocess
If you solve an equation (or in this case,
a system of equations) using substitution,
you can then validate your answer using
elimination.
Solve by
substitution
5
3
5
3
(3 )
5
3 2 5
2 2
1
3 3 1 4
(4,1)
x y
x y
x y
x
y
y y
y
y
y
x
y
+ =
− =
+ =
= +
+ + =
+ =
=
=
= + = + =
Validate by
elimination
5
3
2 8
4
5
4 5
1
(4,1)
x y
x y
x
x
x y
y
y
+ =
− =
=
=
+ =
+ =
=
4.4 Validation