Algebra 1

Lesson 8.2

Substitution Method

Substitution

Method

Whadda ya know 'bout...

$3.50 $7.50

how much does each item cost?

fries = $1.50

burger= $1

Goal:

Use substitution to solve a system of linear equations.

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)

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)

Figure out the solution by using the

guess and check method!

System of equations:

3x - 4y = 17x = 2y + 5

SUBSTITUTION

METHOD,

FTW!

A.E.P.

L.F.

I.N.

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

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)

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...

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)

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

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

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

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