Download 3.2.1 Solve a system using the substitution method 3.2.2 Use

3-2
Using Algebraic Methods to Solve Systems
LEARNING GOALS FOR LESSON 3.2
3.2.1 Solve a system using the
substitution method
3.2.2 Use elimination to solve a
system
3.2.3 Classify the number of solutions
3.2.4 Model and solve real-world
problems with a system of equations
3-2
Using Algebraic Methods to Solve Systems
Example 1: Solving Linear Systems by SUBSTITUTION
Use substitution to solve the system of equations.
Step 1 Solve one equation for one variable.
Step 2 Substitute the expression into the other equation and solve.
Step 3 Substitute the x-value into one of the original equations to
solve for y.
Step 4: Write the solution.
3-2
Using Algebraic Methods to Solve Systems
Example 1: Solving Linear Systems by SUBSTITUTION
Use substitution to solve the system of equations.
" y + 1= 2x
#y = x − 1
A. $
B. #
$3x + 2y = 26
%x + y = 7
€
3-2
Using Algebraic Methods to Solve Systems
Example 2: Solving Linear Systems by ELIMINATION
Use elimination to solve the system of equations.
#
B. $3x + 5y = −16
#
A. $3x + 2y = 4
%3y + 2x = −9
% 4x − 2y = −18
€
3-2
Using Algebraic Methods to Solve Systems
Example 3: Solving Systems with Infinitely Many or No Solutions
Classify the system and determine the number of solutions.
#3x + y = 1
A. $
%6x + 2y = −18
"2x − 4y = 6
B. #
$−3x + 6y = −9
3-2
Using Algebraic Methods to Solve Systems
Example 4: Applications
You can use any method you choose to solve story problems,
but you must always show the equations you used.
A. A veterinarian needs 60 pounds of dog food that is 15% protein.
He will combine a beef mix that is 18% protein with a bacon mix that
is 9% protein. How many pounds of each does he need to make the
15% protein mixture?
B. City Park Golf Course charges $20 to rent golf clubs plus $55 per
hour for golf cart rental. Sea Vista Golf Course charges $35 to rent
clubs plus $45 per hour to rent a cart. For what number of hours is
the cost of renting clubs and a cart the same for each course?