This section discusses solving linear equations with multiple unknown variables for a specified variable. It provides steps to isolate the variable being solved for by rearranging terms on each side of the equation using properties of equality. Examples show solving equations for variables like x, y, a, b, m, and p by moving all other variables and constants to the opposite side of the equation. Practice problems are assigned for the reader to solve equations for specified variables.

1. Unit 1:
Algebraic Operations
Chapter 2: Linear Equations and Formulae

2. Solving Equations
1.2.3 Solve a linear equation with
multiple unknowns for any variable
• Given a linear equation with more than one
unknown, solve for the indicated variable
Workbook p. 71 - 73

3. Solving Equations
for Variables
Example:
Here we must get alone on one side of the
equation.
 Some equations have more than one variable. We
can solve an equation for one variable by
rearranging the equation to get the variable alone
on one side of the equation.
Solve 3 10 forx y x
x

4. To solve for a variable, follow these
steps:
Write the equation
Move the variable you are solving for to the left
side of the equation
Move all other variables and numbers to the
right side of the equation using the properties of
equality.
Solving Equations
for Variables

5. Solving Equations
for Variables
Solve 3 10 forx y x
3 10x y
3 10x y
3 10
1 1
3 3
x y
1
3
10
3
y
x
Example:
Write the equation: x is already
on the left side of the equation
Move y to the right side and change
its sign.
We need x alone, so multiply by to
remove the 3.
This is the answer, because x is
alone on one side of the equation 

6. Solving Equations
for Variables
1
2
Example:
Write the equation: is already
on the left side of the equation
Move to the right side and change
its sign.
We need alone, so multiply by to
remove the 2.
This is the answer, because is
alone on one side of the equation 
Solve 2 3 21 fora b a
2 3 21a b a
2 1 32a b 3b
2 21 3
1 1
2 2
a b a
21 3
2
b
a a

7. Solving Equations
for Variables
5
Example:
Write the equation: is already
on the left side of the equation
Move to the right side and change
its sign.
We need alone, so multiply by to
remove the .
This is the answer, because is
alone on one side of the equation 
m
2
m
m
1
Solve 2 6 for
5
m n m
1
2 6
5
m n
1
6
5
2m n
5 5
1
2 2
5
m n
10 10m n
1
5

8. Solving Equations
for Variables
1
Example:
Write the equation: is already
on the left side of the equation
Move to the right side and change
its sign.
We need alone, so multiply by to
remove the negative.
This is the answer, because is
alone on one side of the equation 
b
3x
b
b
Solve 3 forx b m b
3x b m
3xb m
( ) (( 3) ( ))1 1b m x
3 or
3
b m x
b x m

9. Solving for Variables
Checkpoint p. 72
Solve the equation 6 8 15 for pp q

10. Workbook p. 72 – 73
Solving for Variables