The document discusses the substitution method for solving systems of linear equations. It provides examples of using substitution to solve systems that have a unique solution, no solution, and infinitely many solutions. Step-by-step instructions are given for using substitution to isolate a variable and substitute it into the other equation to solve for the variables.

1. Algebra 1
Lesson 8.2
Substitution Method

2. Whadda ya know 'bout...
Substitution
Method

3. how much does each item cost?
$3.50
fries = $1.50
burger= $1
$7.50

4. Goal:
Use substitution to solve a system of linear
equations.

5. What does it mean to...
"solve a system of linear equations?"
answer: find the solution(s)
y = 4x - 4
y = -2x + 8
the point that is a solution to both lines in the point of intersection, (2,4)

6. Figure out the solution by using the
guess and check method!
System of equations:
2x + y = 20
x + y = 16
the only point that is true for both equations is (4.12)
x
0
1
2
3
4
y
20
18
16
14
12

7. Figure out the solution by using the
guess and check method!
System of equations:
3x - 4y = 17
x = 2y + 5

8. A.E.
I.N.
SUBSTITUTION
P.
METHOD,
FTW!
L.F.

9. Types of solutions:
One Solution
No Solutions
Different slope
Same slope
Infinitely Many
Solutions
Different y-inter.
Different y-inter.
Same slope
ordered pair
false statement
Same y-inter.
identity

10. How to subsitute
System of equations:
3x - 4y = 17
x = 2y + 5
substitute
find y:
SMOTD
3(2y + 5) - 4y = 17
6y + 15 - 4y = 17
2y + 15 = 17
2y = 2
y=1
find x:
x = 2y + 5
x = 2(1) + 5
x=2+5
x=7
answer: (7,1)

11. How to substitute
substitute
SMOTD
Isolate one variable and substitute into...
Equation
ivse-solvse
Equation
eev-say-sol-vee-say
Solve for unknown variable and substitute into...

12. System of equations: One solution (ordered pair)
3x = 2y - 6
x - y = -1
3(y-1) = 2y - 6
3y - 3 = 2y - 6
3x = 2y - 6
y - 3 = -6
3x = 2(-3) - 6
y = -3
3x = -6 - 6
3x = -12
answer:
(-4,-3)
x = -4

13. System of equations: No Solution (false statement)
8x - 4y = 6
2x - y = 9
8x - 4y = 6
8x - 4(2x-9) = 9
8x - 8x + 36 = 9
36 = 9
FALSE STATEMENT- no solution

14. System of equations: Infinitely Many (identity)
3y - 6x = 24
8 + 2x = y
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 + 0 = 24
24 = 24
IDENTITY- infinitely many solutions

15. https://www.youtube.com/watch?v=KNwwu5wjcaA

16. Algebra 1 Reference Guide, Pg. 258, #1-15