Multi-Step Equations
All about Systems of Equations
Graphing
Substitution
Number of Solutions
Word Problems
100
8n=16
n=2
100
What is a LINEAR equation?
An equation that when graphed, creates a straight line.
100
How many solutions are represented in the graph?
1 solution
100
What does the word "substitute" mean?
To exchange/trade/etc.
100
How many solutions can a system of linear equations have?
one, none/zero, or infinitely many solutions
100
Julie is 3 years older than her sister. Julie's age is 11. How old is Julie's sister?
s + 3 = 11 (Julie is 3 years older than her sister)
s = 8
Her sister is 8 years old
Alison
200
3p+8=35
p=9
200
True or False:
It does not matter which method you use when solving systems of linear equations because they will all give you the same answer.
True
200
14) What is the solution to the system of linear equations?
(2,2)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
How many solutions will a set of parallel lines have?
Zero
200
We are at a Seattle Seahawks game. We buy 4 hotdogs and 1 drink. We spend a total of $17. If the drink costs $5, how much does one hotdog cost?
4h + 5 = 17
4h = 12
h = 3 (One hotdog costs $3)
300
4x+27=-x+42
x=3
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point (x and y value of) where the 2 lines intersect.
300
Solve by graphing:
y=-2x+5
y=3x
(1, 3)
300
y=4x
2x-y=5
What is the next step in solving the above system of equations?
2x-(4x)=5
Combine like terms (& solve for x).
300
What is the solution to the system of equations?
y=-2/3x+6
y=6-4/6x
Infinitely many solutions
300
Find the value of two numbers if their sum is 12 and their difference is 4.
4 and 8
400
3h+2+9-h=110-9h
h=9
400
At least how many linear equations will be in a system of linear equations?
At least 2 linear equations
400
Solve by graphing:
y=1/2x -5
y=x+1
(-12, -11)
400
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
400
How many solutions are there for the following system of linear equations? If there is only one solution, what is the solution?
y = 4x + 2x + 1
y = 8x - 9
One solution; (5, 31)
400
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
500
-5(a+3)+6(a+1)+8a=9(a-1)
Infinitely Many Solutions
500
So far we have learned 2 different methods for solving systems of linear equations. What are they?
Graphing and substitution
500
Solve by graphing:
y=2/3x+6
2x+3y=12
(-1.5, 5)
500
Use the substitution method to solve the system of linear equations:
2x+3y=13
y=x+1
(2, 3)
500
How many solutions does this system of linear equations have?
y=-2/3x+6
2x+3y=12
No Solution
500
Mrs. Pastala tells you that the next test is worth 122 points and contains 38 problems. Multiple-choice questions are worth 3 points and word problems are worth 4 points. How many of each type of questions are in there?
8 word problems
30 Multiple Choice