Solving System of Linear Equations by Elimination

I can explain, orally and in writing, how I solved a system using elimination, using

vocabulary like “eliminate,” “coefficient,” and “solution.”

​LANGUAGE OBJECTIVE

I can use elimination to solve a system of linear equations.

​CONTENT OBJECTIVE

LEARNING OBJECTIVES

Poll

How are you feeling today?

• I am feeling tired today.

• I am feeling confused today.

• I am feeling anxious today.

• I am feeling positive today.

Multiple Choice

Two or more equations solved together

• Set of inequalities
• Linear function
• System of equations
• Quadratic equation

Multiple Select

Remove a variable by combining equations

• Elimination

• Substitution

• Graphing

• Function

Multiple Select

Number in front of a variable

• Variable

• Constant

• Term

• Coefficient

Multiple Select

Values that make both equations true

• Solution

• Constant

• Term

• Coefficient

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

Solve using substitution.

• (5, 4)
• (4, 5)
• (-5, 4)

• (-4, -5)

Open Ended

Which step was time-consuming? How could we make it faster? (Graphing or Substitution)

(Talk to your seatmate/groupmate)

What is an Additive Inverse?

The additive inverse of a number is the value that you add to it to get zero.

👉 In other words:

A number and its additive inverse always add up to 0.

Definition

If a number is a, then its additive inverse is −a.

Example:

5 + (-5) = 0 -15 + 15 = 0

STEPS IN SOLVING EQUATIONS USING ELIMINATION

1. Eliminate one variable
   Add or subtract the equations (multiply first if needed) so one variable cancels out.

2. Solve for the other variable
   Solve the equation you get after eliminating a variable.

3. Substitute and check
   Put that value into one of the original equations to find the other variable and check your solution.

Multiple Choice

What is the first step in solving a system of equations?

• Solve for the other variable

• Eliminate one variable

• Substitute and check

Multiple Choice

What is the second step in solving a system of equations?

• Solve for the other variable

• Eliminate one variable

• Substitute and check

Multiple Choice

What is the third step in solving a system of equations?

• Solve for the other variable

• Eliminate one variable

• Substitute and check

Multiple Choice

Which of the following is the correct solution to the system of linear equations?

$$5x+6y=50$$  
$$x-6y=-26$$  

• (6, 10/3)

• (6,5)

• (4,5)

• (4,-5)

Multiple Choice

Solve the system of equations by elimination.

8x−7y=−5

4x−6y=10

• (-5,-5)

• (3,-6)

• (8,7)

• (2,-2)

Multiple Choice

Describe the error in solving the system of equations using elimination:

• They eliminated the x terms when they should have eliminated the y terms.

• They subtracted 5x and x to get 4x, but they should have added the x terms to get 6x = 24.

• They added 16 and 8 to get 24, but they should have subtracted them to get 8 on the right side of the equation.

• They eliminated the y terms, but they couldn't because one is a negative and one is a positive.

Open Ended

“When you solve two equations by graphing, what does the solution represent? How is this similar or different from the solution you get using elimination?”

(Discuss it to your groupmates)

Multiple Choice

Solve by elimination:
-9x - 4y = -20
5x + 4y = 4

• (-4,4)
• (4,4)
• (4,-4)
• (-4,-4)

Multiple Choice

Solve by elimination 
-6x + y = -2
-3x - 6y = 12

• (2,0)
• no solution 
• (0,-2)
• infinite solutions 

Multiple Choice

Solve the system using Multiplication. 
2x + 3y = 12
5x - y = 13

• x = -3, y = -2
• x = 1.5, y = 2
• x = 6, y = 0
• x = 3, y = 2

Open Ended

Reflection: When is elimination faster than substitution? When might substitution be better?