Solving Systems Algebraically
Presentation
•
Mathematics
•
8th - 9th Grade
•
Easy
Katie Argall
Used 7+ times
FREE Resource
9 Slides • 7 Questions
1
Solving Systems Algebraically
2
Today we will
Review what it means to solve a system
Review how to solve by graphing by hand and by computer
Introduce solving by system
3
Open Ended
What does it mean to solve a system of equations?
4
Multiple Choice
On your paper, sketch a graph of the following system and solve:
y=−x−1 y=−4x+2
(-1, -2)
(1, -2)
(1, 4)
(-2, 1)
5
Multiple Choice
Open a new tab or window and go to Desmos.com > click "graphing calculator". Use Desmos to solve the following system:
y=8x−4
y=x+3
(1, -1)
(1, 4)
(4, 1)
(-1, 4)
6
Sometimes, Graphing is inconvenient
No computer
not in "graphing friendly form"
hate graphing
etc.
7
Solving by Substitution
The length of a rectangle is 2 cm more than 3 times its width.
If the perimeter of the rectangle is 28 cm, find its dimensions
8
The length of a rectangle is 2 cm more than 3 times its width.
L = 3w + 2
9
The perimeter of the rectangle is 28 cm
2L + 2w = 28
10
Create the system
L = 3w + 2
2L+ 2w = 28
What do you notice? What do you wonder?
11
Poll
What should we do?
L= 3w+2
Move to slope intercept and graph
Use desmos to do the work for me
I bet there is a better way.
12
Substitution
2L + 2w = 28 and L = 3w + 2
so
2(3w+2) + 2w = 28
(6w+4) + 2w = 28
8w +4 = 28
8w = 24
w = 3
13
Now that we have w....
w = 3 and
L = 3w + 2
L = 3(3) + 2
L = 11
Solution (11, 3)
14
Multiple Choice
Solve
4x − y=−22
y=x+10
(-4, 8)
(2, 8)
(4, 8)
(-4, 6)
15
Multiple Choice
Solve:
y=2x−14
y=−2x+14
(0, 7)
(7, 0)
(0, -7)
(0, 1)
16
Open Ended
What questions do you still have about solving with substitution?
Solving Systems Algebraically
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