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System of Equations
Substitution Method
Day 1
Today’s Objective:
I can solve a system using
substitution.
Solution: An ordered pair that makes the
equation true.
Example:
x+y=7
5+2=7
What are some possible
solutions?
The solutions are always written in
ordered pairs.:
(5,2)
3+4=7
(3,4)
-1 + 8 = 7
(-1,8)
-10 + 17 = 7
(-10,17)
How many
more
solutions
are there?
System of Equations
Definition: a set of two or more equations
that have variables in common.
Any ordered pair that makes ALL
Solution:
the equations in a system true.
Example of
a system:
y = 3x + 1
y = -2x - 4
Solution for this system: (-1,-2)
Verify (check your answer) whether or not the
given ordered pair is a solution for the following
system of equations. (same system as previous
slide)
( -1,-2)
y = 3x + 1
y = -2x -4
( -2) = 3 (-1 ) + 1
( -2 ) = -2( -1 ) - 4
-2 = -3 + 1
-2 = 2 - 4
Is (-1, -2) a solution? explain
YES, because the ordered pair makes
both equations true.
1. Solve for 1 variable
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 (x = or y =)
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
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)
1. Solve for 1 variable
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 =)
x–5=y
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
Step 2
2x – 3y = 7
2x – 3( x – 5 ) = 7
Pg 375
2x – 3x + 15 = 7
11.(2,6)
-1x + 15 = 7
12.(8,11)
-1x = -8
14. (13, -5)
x=8
15. (3,0)
17. (-11,-19)
y=x–5
Step 3
y=x–5
y = (8) – 5
y=3
Step 4
(8, 3)
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
I can solve a system using
substitution.
Assignment:
Pg 375: 11, 12, 14,15, 17
11.(2,6)
12.(8,11)
14. (13, -5)
15. (3,0)
17. (-11,-19)