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System of Equations
Substitution Method
Day 1
Today’s Objective:
I can solve a system using
substitution.
A snack bar sells two sizes of snack packs. A large snack pack is $5 and a
small snack pack is $3. In one day, the snack bar sold 60 snack packs for a
total of $220. How many small snack packs did the snack bar sell?
Identify variables:
Let L = Large packs
Total # of snack packs:
L
Money earned from
snack packs:
5L + 3S = 220
1. Solve for 1 variable
L = 60 - S
+
Let S= small snack packs
S = 60
2. Substitute the variable you just solved for
into the other equation AND solve.
5L + 3S = 220
5( 60 - S ) + 3S = 220
300 – 5S + 3S = 220
300 – 2S= 220
– 2S = -80
S = 40
They sold
40 small
snack packs
What is the solution (ordered pair) that makes both equations true?
x+y=7
x–y =3
Ways to solve:
1. Guess and check
2. Graph them to find the
solution.
3. Tables
4. New method---substitution
x–y=3
x+y=7
x
y
x
y
1. Solve for 1 variable (x = or y = )
2. Substitute the variable you just solved
for into the other equation AND solve.
3. Solve for the other variable (substitute)
4. Write the ordered pair
x+y=7
x–y =3
Step 2
Step 1
x–y=3
+y
+y
x=3+y
Step 3
x+y =7
(3 + y ) + y = 7
3+y+y=7
3 + 2y = 7
-3
2y = 4
y=2
-3
x=3+y
x = 3 + ( 2)
x=3+2
x=5
Step 4
(5, 2)
1. Solve for 1 variable (x= or y = )
2x + 5y = 7
2. Substitute the variable you just solved for
into the other equation AND solve.
x=y–7
3. Solve for the other variable (substitute)
4. Write the ordered pair
Step 1
Step 2
x=y–7
2x + 5y = 7
2( y – 7 ) + 5y = 7
2y – 14 + 5y = 7
7y – 14 = 7
7y = 21
y =3
Step 3
x=y–7
x = (3) – 7
x = -4
Step 4
(-4, 3)
1. Solve for 1 variable
y=x–5
2. Substitute the variable you just solved for
into the other equation AND solve
2x – 3y = 7
3. Solve for the other variable (substitute)
4. Write the ordered pair
Step 1
y=x–5
Step 2
2x – 3y = 7
2x – 3( x – 5 ) = 7
2x – 3x + 15 = 7
-1x + 15 = 7
-1x = -8
x=8
Step 3
y=x–5
y=8–5
y=3
Step 4
(8, 3)
1. Solve for 1 variable
x = 6 - 2y
2. Substitute the variable you just
solved for in to the other
equation AND solve.
5x + 3y = 2
3. Solve for the other variable (substitute)
Step 1
x = 6 – 2y
Homework:
1. (4, 1)
2. (-1, 3)
3. (8,3)
4. (7,2)
5. (12, 9)
1-8
4. Write the ordered pair
Step 2
5x + 3y = 2
5(6 – 2y) + 3y = 2
30 – 10y + 3y = 2
30 – 7y = 2
-7y = -28
y =4
Step 3
x = 6 – 2y
x = 6 – 2( 4 )
x = -2
Step 4
(-2, 4)
x = 6 - 2y
5x + 3y = 2
1. Solve for 1 variable
2. Substitute the variable you just
solved for in to the other
equation AND solve.
3. Solve for the other variable (substitute)
4. Write the ordered pair
Homework:
1-12
1. (4, 1)
7. (3,4)
2. (-1, 3)
8. (2,2)
3. (8,3)
9. (1,8)
4. (7,2)
10. (-4,3)
5. (12, 9)
11. (6,3)
6. (1,-5)
12. (4,-5)
I can solve a system using
substitution.
Assignment:
WS: Substitution 1 #1-5