Graphing Systems of Equations
Substitution to Solve a System
Elimination to Solve a System
Graphing Systems of Linear Inequalities
Word Problems
100
y = 2x + 2
y = x − 1
(-3, -4)
100
y = 2
3x + 2y = 10
(2, 2)
100
x + 3y = 5
2x − 3y = −8
(−1, 2)
100
What does a dotted line mean when graphing linear inequalities?
> or <
200
y = 2x + 4
y = 3x + 2
(2, 8)
200
x = −3y + 2
−x + 2y = 3
(−1, 1)
200
−5y + 8x = −18
5y + 2x = 58
(4, 10)
200
How is graphing systems of inequalities different than graphing systems of equations? (2 things)
Sometimes they use dotted lines and you have to shade for inequalities.
200
Zack and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Zack starts with 20 points, and his little brother starts with 19 points. Zack gets 1 point for every successful shot, and his brother, since he is younger, gets 2 points for each successful shot. Eventually, the brothers will have a tied score in the game.
How many points will they both have?
How many additional shots will each brother have made?
Zack and his brother will both have a score of 21 by making 1 shot.
SUBSTITUTION
Zack: y=20+x
Brother: y=19+2x
300
y = 1/2 x + 2
y = 1/4 x + 4
(8, 6)
300
x − 2y = −10
3x = y
(2, 6)
300
3y − 5x = −26
−2y − 5x = −16
(4, −2)
300
How do you determine a solution to a graphed system of linear INEQUALITIES?
The solution is where the shaded regions overlap.
300
A charity is considering the possibility of having a benefit night at two different restaurants. The owner of the local Italian restaurant has offered to make a donation of $928 and $1 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $44 plus $3 per diner. Based on the number of diners who have promised to participate in the event, it appears that each restaurant would donate the same total amount.
How many diners promised to participate?
How much would each restaurant donate?
With 442 diners promising to participate, each restaurant would donate $1370
Solve with SUBSTITUTION
y=x+928 and y=3x+44
x+928=3x+44
400
x = 3
y = 2x + 1
(3, 7)
400
2x – 3y = –2
y = −4x + 24
(5, 4)
400
3x − 4y = 8
18x − 5y = 10
(0, -2)
400
y ≤ x − 2
y > −3x + 5
Shaded below the first line and to the right of the second line.
400
At a community barbecue, Mrs. Jefferson and Mr. Hall are buying dinner for their families. Mrs. Jefferson purchases 2 hot dog meals and 1 hamburger meal, paying a total of $18. Mr. Hall buys 1 hot dog meal and 1 hamburger meal, spending $14 in all.
How much does each type of meal cost?
Hot dog meals cost $4 each, and hamburger meals cost $10 each.
Solve with ELIMINATION...multiply 2nd eqatu9ion by either -1 or -2...
2x+y=18
x+y=14
500
4x + 2y = 8
2x + y = 4
Every point on 2x+y=4 is a solution.
500
5x − 13 = y
−5x + y = 24
no solution
500
4x−9y = 2
12x−5y = −38
(-4, -2)
500
2x – 3y < 12
x + 5y < 20
Shade above the first line and below the second line.
500
Felix and his friends like to collect and trade cards from a certain combat card game. Felix used his allowance to purchase 8 booster packs and 2 premade decks, which included a total of 138 cards. For his birthday, he received 5 booster packs and 9 premade decks, which included a total of 280 cards.
How many cards come in every booster pack and every premade deck?
Each booster pack has 11 cards, and each premade deck has 25 cards.
Solve using ELIMINATION...multiply both equations by...
8x+2y=138
5x+9y=280