Systems of Equations
Graphically
Graphically
Solve the following system graphically:
y = 2x + 2
y = x - 1
(-3, -4)
Solve the following system algebraically:
y = 2
3x + 2y = 10
(2, 2)
Solve the following system algebraically:
x + 3y = 5
2x -3y = -8
(-1, 2)
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
2 fancy shirts and 5 plain shirts
What does a dotted line mean when graphing linear inequalities?
> or <
Solve the following system graphically:
y = 2x + 4
y = 3x + 2
(2, 8)
Solve the following system algebraically:
x + 3y = 2
-x + 2y = 3
(-1, 1)
Solve the following system algebraically:
-5y + 8x = -18
5y + 2x = 58
(4, 10)
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
small box of oranges = $7
large box of oranges = $13
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.
Solve the following system graphically:
x = 3
y = 2x + 1
(3, 7)
Solve the following system algebraically:
x - 2y = -10
3x - y = 0
(2, 6)
Solve the following system algebraically:
3y - 5x = -26
-2y - 5x = -16
(4, -2)
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of one senior citizen ticket and one child ticket?
senior citizen ticket = $4
child ticket = $7
How do you know if a point is a solution to a system of inequalities?
Plug in the x-coordinate (x-value) and the y-coordinate (y-value) into BOTH inequalities to see if they make BOTH inequalities true.
Solve the following system graphically:
4x + 2y = 8
2x + y = 4
All points along 4x+2y =8
Solve the following system algebraically:
2x – 3y = –2
4x + y = 24
(5, 4)
Solve the following system algebraically:
3x−4y=8
18x−5y=10
(0, -2)
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
6 chickens and 7 pigs
Solve the following system of inequalities graphically:
y≤x−2
y>−3x+5
Then state an ordered pair in the solution set.
Answers will vary.
Solve the following system graphically:
y = 1/2 x + 2
y = 1/4 x + 4
(8, 6)
Solve the following system algebraically:
5x - y = -13
-5x +2y = 24
(-2/5, 11)
Solve the following system algebraically:
4x−9y−2=0
12x−5y+38=0
(-4, -2)
A 100 foot cable is cut into two pieces. The first piece is 18 feet longer than the second piece. How long is each piece of cable?
59 feet and 41 feet
Solve the system of inequalities graphically:
2x – 3y < 12
x + 5y < 20
Is the point (5, 3) in the solution set?
NO! The point (5, 3) is right on the line and it is dotted so it is NOT included!
Plug in values: 1 < 12 20 < 20