ZONK Review
1. Find the solution to the following system
of equations by graphing:
2. Graph the system of inequalities and
name three points in the solution set.
−4𝑥 + 𝑦 = −5
𝑦 = 4𝑥 + 3
𝑥≤2
6𝑥 − 3𝑦 < 12
Change the first
equation to
y = 4x – 5.
x – int: 6x = 12
x=2
y – int: -3y = 12
y = -4
Then graph using
y = mx + b.
Example Points:
(-1, 0) (-2, 2) (-4, 5)
NO SOLUTION
3. Solve the following system
using SUBSTITUTION.
4. Solve the following system
using ELIMINATION.
6x – 5y = 76
-3x + 5y = -43
−2𝑥 + 6𝑦 = −8
9
𝑥 = 2𝑦 + 3
9
9 2
−2 (2 𝑦 + 3) + 6𝑦 = −8
𝑥 = 2 (3) + 3
3x + 0 = 33
-9y – 6 + 6y = -8
-3y – 6 = -8
-3y = -2
2
𝑦=3
𝑥 = 6 +3
x=3+3
x=6
x = 11
18
𝟐
(6, 𝟑)
Add Equations
6(11) – 5y = 76
66 – 5y = 76
- 5y = 10
y = -2
(11, -2)
5. There are 400 turtles competing in the Turtle Grand Prix. It cost each turtle $20 to register for
the 5k race and $35 to register for the 10k race. If the Turtle Grand Prix brought in $10,340 in
registration fees, how many turtles ran each distance?
f – # of turtles in the five K race
t - # of turtles in the ten K race
20f + 35t = 10, 340
f + t = 400
- t = -t
So f = 400 – t USE SUBSTITUTION
20(400 – t) + 35t = 10,340
8,000 – 20t + 35t = 10,340
8,000 + 15t = 10,340
15t = 2,340
t = 156
f = 400 – (156) = 244
244 registered
for the 5K and
156 registered
for the 10K.
6. Turtles who signed up for the annual Turtle Grand Prix for the very first time received three
free T-shirts. Those turtles who were returning runners only received one free t-shirt. The
difference between the number of first time runners at the 5k and the number of returning
runners was 60. If they gave away a total of 548 free t-shirts, how many turtles were first time
runners?
f - # of first time runners
r - # of returning runners
3f + 1r = 548
f - r = 60
+r=+r
So f = 60 + r. USE SUBSTITUTION
3(60 + r) + r = 548
180 + 3r + r = 548
180 + 4r = 548
4r = 368
r = 92
152 first time runners
92 returning runners
f = 60 + 92 = 152
7. Solve the following system
using SUBSTITUTION.
8. Solve the following system
using ELIMINATION.
3x + y = 8 so y = -3x + 8
4x + 6y = 6
4x + 6(-3x + 8) = 6 y = -3(3) + 8
4x – 18x + 48 = 6
y = -9 + 8
-14x + 48 = 6
y = -1
-14x = - 42
x=3
(3, -1)
(-3x + 3y = 12) ∙ 4
(4x + 2y = 20) ∙ 3
-12x + 12y = 48
12x + 6y = 60____
18y = 108
y=6
-3x + 3(6) = 12
-3x + 18 = 12
-3x = -6
x=2
(2, 6)
9. Spectators at the Turtle Grand Prix can purchase Turtle Trax Ice Cream Cones at the
concession stand. The difference between the price of the waffle cone and the price of the
regular cone is $0.75. If a family of seven purchased three waffle cones and four regular
cones for a total of $28.50, how much was the cost of a single waffle cone?
w - price of a waffle cone.
r – price of a regular cone.
Use elimination to eliminate
the r because you only need to
find the price of the waffle cone.
(w – r = .75) ∙ 4
3w + 4r = 28.50
4w – 4r = 3____
7w
= 31.50
w
= $4.50
10. Find the solution to the following system
of equations by graphing:
1
4
1
𝑥 + 4 𝑦 = −1
3𝑦 = 𝑥
(-3, -1)
A single waffle cone is $4.50
11. Graph the system of inequalities and
name three points in the solution set.
3
−𝑥 + 2 𝑦 > −3
𝑦 ≤ −𝑥
Ex Points:
(-2, 0) (-3, 1) (-4, 2)
Directions: Solve the following systems using SUBSTITUTION OR ELIMINATION.
12.
3x + 4y = 9
4y – 3x = -1 Line up the x’s and y’s!
3x + 4y = 9
-3x + 4y = -1
8y = 8
y=1
3x + 4(1) = 9
3x + 4 = 9
𝟓
( ,1)
13.
(3x + 4y = 2) ∙ -3
9x + 12y = 6
-9x – 12y = -6
0+0=0
Infinitely Many Solutions
3x = 5
𝟑
5
x=3
14. Tammy Turtle is going to the concession stand with 11 coins that total exactly $2.00. If her
coins are all quarters and dimes, how many of each coin does she have?
q = # of quarters
d = # of dimes
Use Elimination
(q + d = 11) ∙ -.25
.25q + .1d = 2.00
-.25q - .25d = -2.75
-.15d = -.27
d=5
q + 5 = 11
q=6
5 dimes and 6 quarters
15. The race is on! Tony the Turtle got a good start. He has already gone 11 feet, and he is
currently traveling at a rate of three feet per minute. Tammy the Turtle woke up late and is just
now starting the race, but she’s determine to catch up and is traveling at a rate of 3.5 feet per
minute. How many minutes will it take for Tammy to Catch up to Tony? How far will they
have traveled at that time?
Let m = # of minutes
And d = distance traveled
Tony:
Tammy:
d = 3m + 11
d = 3.5m
Substitution:
3.5m = 3m + 11
.5m = 11
m = 22
d = 3.5(22) = 77
They will have both gone 77 feet after 22 minutes.