2. Systems of Equations Today:
a. Elimination (3)
b. Substitution (2)
c. Solving Systems: Word Problems (2)
3. Question:
Do you have Friggatriskaidekaphobia?
from Greek tris meaning "3", kai meaning "and",
deka meaning "10" phobos meaning "fear" or "morbid fear"
"Frigg" is the Norse goddess whom Friday is named after
An extraordinary fear of Friday the 13th
Answer honestly...
4.
5.
6.
7.
8.
9.
10. Determine whether the ordered pair is
a solution of the given system.
The ordered pair (5, 2) makes both equations true.
(5, 2) is the solution of the system.
Substitute 5 for x and 2
for y in each equation in
the system.
2 – 2 0
0 0
0
3(5) – 2 13
15 – 2 13
13 13
3x – y 13
(5, 2);
3x – y = 13
𝟐
𝟓
x – y = 0
𝟐
𝟓
x – y = 0
11. (–2, 2); x + 3y = 4
–x + y = 2
–2 + 3(2) 4
x + 3y = 4
–2 + 6 4
4 4
–x + y = 2
– (–2) + 2 2
4 2
Substitute –2 for x and 2 for y in
each equation in the system.
The ordered pair (–2, 2) makes one
equation true but not the other.
(–2, 2) is not a solution
of the system.
If an ordered pair does not satisfy the first equation in the
system, there is no reason to check the other equation(s).
Helpful Hint
12. SOLVING SYSTEMS BY ELIMINATION:
1. Arrange the like variables in columns.
2. Pick a variable, x or y, and make the two
equations opposites using multiplication.
3. Add the equations together (eliminating a
variable) and solve for the remaining variable.
4. Substitute the answer into one of the
ORIGINAL equations and solve.
5. Check your solution.
13. 5x - 4y = -21
-2x + 4y = 18
We need to eliminate (get rid of) a variable by cancelling out
one of the variables. We then solve for the other variable.
3x + 0 = -3
x = -1
THEN----
Like variables must be lined under each other.
What should we eliminate first?
Solve: By Elimination
Do we add or subtract the two equations?
14. 5x - 4y = -21
(-1, 4)
Substitute your first
solution into either original
equation and solve for the
second variable.
The solution to this system
of equations is:
Now check your answers in
both equations------
5(-1) – 4y = -21
-5 – 4y = -21
5 5
-4y = -16 y = 4
16. We have two options; what are they?
x + y = 30
x + 7y = 6
We need to eliminate (get rid of) a variable. To simply
add this time will not eliminate a variable.
a. Subtract
b. Multiply one of the
equations by -1, then add
SOLVING SYSTEMS BY ELIMINATION:
17. x + y = 30
x + 7y = 6( )-1 -x – 7y = - 6
Now add the two
equations and solve.
-6y = 24
- 6 - 6
y = - 4
THEN----
x + y = 30
18. x + y = 30
(34, - 4)
Substitute your answer
into either original
equation and solve for
the second variable.
Solution
Now check your answers in
both equations------
x + - 4 =30
+4 +4
x = 34
20. SOLVING SYSTEMS BY SUBSTITUTION:
1. Solve one of the equations for x or y.
2. Substitute your new expression from Step
1 into the other equation and solve for the
variable.
3. Plug that solved variable into the other equation
from Step 1 and solve for the other variable.
4. Check your answers by plugging it into the
original equations.
- Get x or y by itself.
21.
22. SOLVING SYSTEMS WORD PROBLEMS:
Kelly went back-to-school shopping this weekend. She
spent $160 on jeans and shirts. She bought a total of
12 items, with jeans costing $16 and shirts costing $12.
How many jeans and shirts did she buy?
1. Mark
the text.
2. Label
variables.
j = jeans
s = shirts
3. Create
equations.
16j + 12s = 160
What’s the 2nd equation?j + s = 12
4. Solve.
5. Check.
23. Mrs. Smith took her family and friends to
the movies. There were a total of 12 people.
Children tickets cost $5 and adult tickets cost
$10. She spent a total of $95. How many adults
& how many children went to the movies?
1. Mark
the text.
2. Label
variables.
3. Create
equations.
4. Solve.
5. Check.
