Example #2
View the prompt below:
If
y
= 1
, evaluate the following expression:
14 
y
14 
y
= 14 
(
1
)
= 13
If
y
= 1
,
14 
y
= 13
If
b
= 20
, evaluate the following expression:
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b
b
b
3.08 Substitution for Multiple Variables
Substitution for Multiple Variables
We've seen mathematical expressions that have multiple variables. Some examples are:
Mathematical Expressions with Multiple Variables
x

y
3
a
+ 3
b
3(
P
) · (3
S
) + 1
a
2
+
b
2
+
c
2
Substitution for One Variable
We can use the substitution method on these expressions, similar to an expression containing only one variable. If a variable's value is
specified, we can substitute the variable with its value:
Using a Calculator for Operations with Multiple Variables
When performing operations with known variables, a calculator is a
great resource to evaluate expressions and to check your work. Input
your operations, including parentheses, to perform calculations.
If
x
=  4
and
y
= 9
, what is
8
(
x
)
+
(
72 ÷ y
)
?
Step 1:
Rewrite your expression with the knowledge that
x
=  4
and
y
= 9
.
8
(
x
)
+
(
72 ÷ y
)
= 8
(
4
)
+
(
72 ÷ 9
)
First perform the operation within the parentheses.
Step 2:
Perform the operation
72 ÷ 9
on your calculator by typing "
72 ÷ 9
" and then clicking the "
=
" button. Record the quotient,
8
. Now we see that our expression is equal to
8
(
4
)
+
(
8
)
.
If
b
= 5
,
(
3a
)
+
(
3b
)
=
(
3a
)
+
(
3 · 5
)
=
(
3a
)
+ 15
Copyright © 2018 MindEdge Inc. All rights reserved. Duplication prohibited.
You need to clear the screen before entering more information. So, after
recording the quotient, click the clear button. Depending on your
calculator, this button might say
AC
,
C
,
CE
, or
Clear
.
Step 3:
Perform the operation
8
(
4
)
on your calculator by typing "
8 × 4
" (using the minus sign for
negative
)
and then clicking
=
. Record the product,
32
. Now we see that our expression is equal to
32 +
(
8
)
Step 4:
Perform the final operation,
32 + 8
, on your calculator by entering "
32 + 8
." The final answer is
24
.
Here, we see that after we substitute
b
with its value,
5
, the expression is equal to "
(3
a
) + 15
." Notice that we did not substitute for the variable
a
because we do not know the value of this variable. Therefore, the variable
a
remains in the expression, even after evaluation. In the following section, we will explore how to evaluate an expression when multiple
variables have known values.
Substitution for Multiple Variables
When multiple variables each have specified values, we can substitute each variable with its respective value. For example: