General Systems
Y-intercept
What are the 3 different types of Graphs?
Non Intersecting (Non Parallel), Parallel, and Intersecting
With the substitution method, which variable should you solve for first? Explain.
You should solve for a variable that's already solved for or have a coefficient of 1 and -1
When is the Best time to use the Elimination method when solving Systems?
When you have Common Coefficient.
Russell and his good buddy Ian are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Russell has already finished 3 oil changes today, and can complete more at a rate of 1 oil change per hour. Ian just came on shift, and can finish 2 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Russell and Ian each have done? Write the following systems.
y = x + 3
y = 2x
In the Slope Intercept Formula, the "m" is considered as...
Slope
What is the first step in Graphing Systems?
Graph the b or y-intercept in the equation
Solve the following system of equations using substitution. What is the value of y?
2x + 3y = 105
x + 2y =65
25
If you do not have equal coefficients for both variables, can you still use the elimination method? Explain.
You can use the elimination method by multiplying one or both equations by a constant.
Two classmates have decided to read all the volumes in a popular series of books. Lucy has already read 8 volumes and will continue to read new ones at a rate of 1 volume per week. Maria, who hasn't started reading the series yet, will read 3 volumes per week. At some point, Maria will catch up with Lucy and they will be reading the same book. How long will that take? How many volumes will each girl have read by then?
In 4 weeks, the girls will each have read 12 volumes in the series.
In the Standard Form Formula, "A and B" are considered to be....
Coefficients
What are the 4 different types of Lines?
Vertical, Horizontal, Slope intercept, and Standard Form.
Solve the following System using Substitution.
y = -2x + 5
3y = -x - 5
(4, -3)
Write a system of equations that can be solved using elimination without multiplication.
Answers may vary
Th ere were 155 people at the basketball game. Tickets for the game are $2.50 for students and $4 for adults. If the total money received for admission was $492.50, how many students and adults attended the game?
85 students and 70 adults
What are the 3 Methods of systems of Linear Equations?
Graphing, Substitution, Elimination
Graph the following Systems and State the Solution
y = 2x + 1
y = -4x + 7
One Solution; (1, 3)
Solve the following Systems using Substitution.
4x + y = 0
2x - y = -12
(-2, 8)
Solve the following systems using Linear Combination.
x + 2y = 3
x - y = 6
(5, -1)
Jocelyn has $1.95 in her pocket made up of 27 nickels and dimes. How many of each type of coin does she have?
12 dimes and 15 nickels
Is the Ordered Pair of (1, 2), satisfy the Systems of
y = -x + 3 and y = 4x - 2....... Must Show Work
Yes
Graph the Following Systems and state it's solution.
18x - 3y =21
-y = -6x + 7
Infinite Solutions
One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?
8
Solve the following systems using Linear Combination.
x - 3y = 1
2x + 2y = 10
(4, 1)
During a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. Later you return to the same store and buy three more sweatshirts and four more pairs of sweatpants for $123. What is the sale price of each sweatshirt and each pair of sweatpants?
sweatshirt: $16; sweatpants: $18.75