
Solving Systems by Elimination
Presentation
•
Mathematics
•
6th - 8th Grade
•
Practice Problem
•
Medium
+1
Standards-aligned
Santiago Villarreal
Used 11+ times
FREE Resource
9 Slides • 14 Questions
1
Solving Systems by Elimination
Objective: Solve a system of equations by elimination
2
System of Equations: a collection of two or more equations with the same set of unknowns (variables).
Example:
4x - y = -6
5x + y = -21
3
Multiple Choice
At what point do these two lines cross?
(3,4)
(4,3)
(-3,4)
(-4,3)
(3,-4)
4
2x - y = 2
x + y = 7
EXAMPLE
What if we don't have a graph.
5
Line up the x, the y, and the equal sign.
Look to see if the variables are the same/opposite.
If YES - Move to Step 3
If NO. - Multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.
Add or Subtract the TWO equations to eliminate one of the variables.
Solve for the remaining variable
Substitute your answer in one of the original equations
Check your answer.
Write final answer as an ordered pair.
STEPS TO SOLVE
6
Let's Explore Each Step
line up the x & y & the equal sign.
7
Multiple Choice
Look at the system below. Is the x & y lined up?
3x=4y−7
3x+7y=11
YES
NO
8
Multiple Choice
Is the System Lined up?
4y − 3x=12
y+3x=0
No
YES
9
Let's Explore Each Step
ONE VARIABLE MUST BE ELIMINATED!!!!!!!!!
10
Multiple Choice
-4x + 2y = -30
Which variable will be eliminated?
11
Let's Explore Each Step
look to see if any of the coefficients are the same/opposite.
12
Multiple Choice
Are any of the coefficients same or opposite?
2x - 6y = 20
2x + 5y = -11
Same
Opposite
Neither
13
Multiple Choice
Are any of the coefficients same or opposite?
x - y = 11
2x + y = 19
Same
Opposite
Neither
14
Multiple Choice
Are any of the coefficients same or opposite?
4x+ 9y = 28
-4x -y = -28
Same
Opposite
Neither
15
Let's Explore Each Step
Add or Subtract the TWO equations to eliminate one of the variables.
16
Multiple Choice
9x-3y=-3
-5x+3y=-1
Would you add or subtract to eliminate the variable (Get ZERO)
ADD
SUBTRACT
17
Multiple Choice
10x-8y=-30
-10x+9y=25
Would you add or subtract to eliminate the variable (Get ZERO)
ADD
SUBTRACT
18
Let's Explore Each Step
If NO. - multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.
19
Multiple Choice
4x-6y= -6
-2x-12y= -12
20
Multiple Choice
2x+9y= -7
6x-3y= 9
21
Multiple Choice
Macy starts with $20 in her bank account and she saves $5 each week. Robby has $100 in his bank account, and he saves $2.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts and how much money will that be? Write a system of equations to solve.
25 weeks; $160
32 weeks; $180
20 weeks; $120
22 weeks; $135
22
Multiple Choice
Ride and Transport are two new ride sharing companies in Colorado. Ride is charging $2 for pick up fees and then $2.50 per mile. Transport is charging only $2.70 per mile. How many miles will it take for both companies to charge the same amount? Write a system of equations to solve.
27 miles
10 miles
270 miles
100 miles
23
Poll
How are you feeling about this topic (elimination) so far?
I understand!
I need more practice, but I'm getting it
I do not know where to begin
Solving Systems by Elimination
Objective: Solve a system of equations by elimination
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