AFDA – Unit 2: Linear Functions Pt 2
Day 6 Notes: Substitution
Name: _________________
Block: _____ Date:_______
Today you will…
 solve systems of equations using substitution
 solve word problems using substitution
1. Solve ______ equation for ______ variable (which ever is easiest).
2. _________________ into the other equation.
3. Solve for the ___________________ variable.
4. Substitute back into the ________________ _______________ to solve for the
remaining variable.
5. __________ __________ __________ in BOTH equations!
6. Write solution as an __________________ _____________.
Example.
𝑥 + 3𝑦 = 2
{
2𝑥 − 3𝑦 = 22
1. Solve for x
𝑥 + 3𝑦 = 2
in the first
−3𝑦 − 3𝑦
equation by
𝑥 = −3𝑦 + 2
subtracting
3𝑦 from both
sides.
4. Substitute
(−2) for 𝑦
into the
original
equation
and solve
for 𝑥.
𝑥
𝑥
𝑥
𝑥
= −3𝑦 + 2
= −3(−2) + 2
=6+2
=8
2. Substitute
(−3𝑦 + 2)
for 𝑥 in the
second
equation.
2(−3𝑦 + 2) − 3𝑦 = 22
5. Plug in 8 for
𝑥 + 3𝑦 = 2
𝑥 and −2 for 8 + 3(−2) = 2
𝑦 in both
2=2
equations to
check
2𝑥 − 3𝑦 = 22
solution.
2(8) − 3(−2) = 22
22 = 22 
3. Solve for 𝑦.
2(−3𝑦 + 2) − 3𝑦 = 22
−6𝑦 + 4 − 3𝑦 = 22
−9𝑦 + 4 = 22
−4 − 4
−9𝑦
18
=
−9
−9
𝑦 = −2
6. Write as a
cooridnate
pair.
(8, −2)
Guided Practice.
3𝑦 − 𝑥 = 0
1. {
𝑥 − 4𝑦 = −2
2𝑥 − 3𝑦 = −2
2. {
4𝑥 + 𝑦 = 24
Special Cases.
2𝑥 − 𝑦 = 3
1. {
2𝑦 = 4𝑥 − 6
𝑥 − 2𝑦 = 3
2. {
2𝑥 − 4𝑦 = 7
Word Problems.
The perimeter of a rectangular wooden deck is 90 sq ft. The deck’s length is 5 feet
less than 4 times its width. Write a system of linear equations that can be used to
determine the length, L, and width, W, of the wooden deck, then solve the system
using substitution. (Remember, the formula for perimeter is 𝑃 = 2𝐿 + 2𝑊)
A group of 28 people attended the fieldtrip. The number of teachers on the fieldtrip
was 20 less than the number of students. Write a system of equations that describes
the number of teachers, t, and the number of students, s, that went on the fieldtrip,
then solve the system using substitution.
Extra Practice.
𝑥 =𝑦+3
1. {
3𝑥 − 2𝑦 = 4
1
𝑦 = 𝑥−4
2
3. {
5𝑥 − 2𝑦 = 3
𝑥 − 2𝑦 = −1
2. {
4𝑥 − 3𝑦 = 6
𝑥−𝑦 =5
4. {
2𝑥 − 5𝑦 = 4