notes 7.4 solving linear systems by substitution.notebook · 2018-04-09 · notes 7.4 solving...

Notes 7.4 Solving Linear Systems by Substitution.notebook April 09, 2018

Section 7.4Solving Systems of Linear

Equations by the Substitution Strategy

Why would graphing not always be an appropriate method to use when solving a

system of linear equations?

time consuming to draw a graph

graph may be too big to graph by hand

answer may have to be approximated from the graph

somepossibleanswers

Therefore, we need another method to use instead of graphing. This other method is called Solving by Substitution or the Substitution Method.

We use substitution to simplify a question like

4x + 3y when x = 2 and y = 4

Remember that we can also substitute numbers into variables in equation to check whether ordered pairs are a solution to an equation.

Now we are going to use substitution in a different way.


Type #1 Question

Ex(1) Solve these systems of linear equations by using the substitution method.

Exercises: Section 7.4 Basic Substitution Type Questions Worksheet


Type #2 Question

Ex(2) Solve these systems of linear equations by using the substitution method.

Sometimes you are not automatically given one of the coordinates

How can you check your answer?



y = x + 1y = 3x 1

Option #1:Substitute values back into original equations

Option #2:Graph the linear system

4 3 2 1 0 1 2 3 4 5

3

2

1

1

2

3

x

y





5 4 3 2 1 0 1 2 3 4 5

5

4

3

2

1

1

2

3

4

5

x

y

Exercises: Page 425 # 4


Ex(3) Solve these systems of linear equations by substitution.

Choose to solve for the variable

that has a coefficient of 1.

(number in front of the variable)

10 9 8 7 6 5 4 3 2 1 0

5

4

3

2

1

1

2

3

4

5

6

7y




Type #3 Question


Exercises: Page 425 # 5


Section 7.1 Let's write some Systems of Linear Equations

Ex(1)The total number of states in Austria and Germany is 25. Germany has 7 more states than Austria. What is the number of states in each country?

Ex(2)The total mass of vitamin C in one apple and two peaches is 17 mg. The total mass of vitamin C in two apples and one peach is 13 mg. What is the mass of vitamin C in each fruit?

Ex(3)For a puppet play at the library, tickets for adults and tickets for children were sold. The total number of tickets sold was 256. Tickets for adults cost $5 each and tickets for children costs $2 each. The total receipts were $767. How many of each type of ticket were sold?

Now, let's try some word problems where you need to set up the system of linear equations and then solve by substitution.


Exercises: Page 425 426 # 10, 11, 13, 14 OR Do stations with Worksheet Questions

notes 7.4 solving linear systems by substitution.notebook · 2018-04-09 · notes 7.4 solving...

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