alg1 8.2 substitution method
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Algebra 1
Lesson 8.2
Substitution Method
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Substitution
Method
Whadda ya know 'bout...
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$3.50 $7.50
how much does each item cost?
fries = $1.50
burger= $1
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Goal:
Use substitution to solve a system of linear equations.
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y = 4x - 4
y = -2x + 8
What does it mean to...
"solve a system of linear equations?" answer: find the solution(s)
the point that is a solution to both lines in the point of intersection, (2,4)
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Figure out the solution by using the
guess and check method!
2x + y = 20x y
0 201 182 163 144 12
System of equations:
x + y = 16 the only point that is true for both equations is (4.12)
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Figure out the solution by using the
guess and check method!
System of equations:
3x - 4y = 17x = 2y + 5
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SUBSTITUTION
METHOD,
FTW!
A.E.P.
L.F.
I.N.
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Types of solutions:
One Solution
Different slope
Different y-inter.
No Solutions
Same slope
Different y-inter.
Infinitely Many Solutions
Same slope
Same y-inter.ordered pair false statementidentity
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3x - 4y = 17
How to subsitute substituteSMOTDSystem of equations:
x = 2y + 5
3(2y + 5) - 4y = 17
6y + 15 - 4y = 17
2y + 15 = 17
2y = 2
y = 1
find y:
find x:x = 2y + 5
x = 2(1) + 5
x = 2 + 5
x = 7
answer: (7,1)
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How to substitute substituteSMOTD
ivse-solvseeev-say-sol-vee-say
Equation Equation
Isolate one variable and substitute into...
Solve for unknown variable and substitute into...
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3x = 2y - 6System of equations: One solution (ordered pair)
x - y = -1
3(y-1) = 2y - 6
3y - 3 = 2y - 6
y - 3 = -6
y = -3
3x = 2y - 6
3x = 2(-3) - 6
3x = -6 - 6
3x = -12
x = -4answer:
(-4,-3)
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8x - 4y = 6System of equations: No Solution (false statement)
2x - y = 9
8x - 4y = 6
8x - 4(2x-9) = 9
8x - 8x + 36 = 9
36 = 9
FALSE STATEMENT- no solution
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3y - 6x = 24System of equations: Infinitely Many (identity)
8 + 2x = y
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 + 0 = 24
24 = 24
IDENTITY- infinitely many solutions
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Algebra 1 Reference Guide, Pg. 258, #1-15
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