System of Equations: Substitution Method

Algebra 1

Using Substitution to Solve Linear Systems

Teacher Facing
November 14, 2023

Day 1

Do Now

Graph and identify the solution to the system. Show your work.

1) x = 8

6 + y = x

2) 6x - y = 4
-4x - y = +1

​

LO: SWBAT use substitution to solve systems
consisting of two linear equations with two variables.

DOL: Given 5 problems, students will correctly use
substitution to solve systems consisting of two linear equations with two variables in at least 4 of 5
questions.

TEKS: A.5C Solve systems of two linear equations with two variables for mathematical and real-world problems.

Lesson Vocabulary

Answer the

essential question
on a response card.

System of linear equations

Substitution

y = 2x + 7

3y +4x = 9

3( 2x + 7 ) + 4x = 9

Substitute

Today you will learn how to solve
system of linear equations by …

By Substituting

Step 1:
Isolate a variable.

Step 2:
Substitute the
expression into the
2nd equation.

Step 3:
Solve the new
equation.

Step 4:
Substitute the known
variable into either
equation to solve for
the other variable.

Solving System of Equations Substitution

​Step 1: Isolate a variable
Step 2: Substitute
Step 3: Solve
Step 4: Substitute

​Let's try one together...

Step 1:
Isolate a
variable

Multiple Choice

Isolate the y to equation $$x+y=-2$$

• $$y=x+2$$

• $$y=x-2$$

• $$y=-x-2$$

• $$y=-x+2$$

​Let's try one together...

​Step 2: Substitute the expression into the second expression

Hotspot

Knowledge Check: Where will I substitute the new equation?

​Let's try one together...

​

​Step 3: Solve the new equation

Math Response

Solve for x.

$$4x-\left(-x-2\right)=-3$$

(just the number)

Type answer here

Correct Answer: -1

Deg^°

Rad

​Let's try one together...

​

​Step 4: Substitute the known variable into either equation to solve for the other variable.

Math Response

After substitution, what would be the new equation for y?

Type answer here

Correct Answer: y=-\left(-1\right)-2

Deg^°

Rad

​Let's try one together...

​

​Solution (-1, -1)

Reorder

Sally missed today's lesson. Provide Sally with the steps of Substitution method to solve a system of equations.

• Isolate the variable

• Substitute the expression into the 2nd equation

• Solve the new equation

• Substitute the known variable into either equation to solve for the other variable

1

2

3

4

• 1
• 2
• 3
• 4

Demonstration of Learning

DOL Given 5
problems, students
will correctly use
substitution to solve
systems consisting
of two linear
equations with two
variables in at least
4 of 5 questions.

Open Ended

Suppose you graph a system of equations, but the point of intersection is not clear from the graph. How can you determine the solution from the system?

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