Solve Systems by Graphing
Solve the system by graphing
y=1.5x-5
y=x-3
(4,1)
Solve the system using substitution
y=1/2x-5
x+3y=20
(14,2)
Solve the system using elimination
x+5y=19
-x-2y=-4
(-6,5)
How do you know if there are no solutions based on a graph AND two equations?
Graph: They are parallel lines
Equations: Same slopes but different y-intercepts
Two angles are complementary. The larger angle is 36 more than the smaller angle. What is the measure of the larger angle?
Tip: Complementary angles are angles that sum up to 90 degrees.
63 degrees
Solve the system by graphing
y=6
y=3x-3
(3,6)
Solve the system using substitution
x+y=8
3x+2y=8
(-8,16)
Solve the system using elimination
4x-8y=-4
-2x+8y=-2
(-3,-1)
Ralph's t-shirt company sells custom t-shirts for $5.00 each plus a $20 shipping and design fee. Frank's t-shirt company sells t-shirts for $10 each with no additional fees. Let x represent the number of shirts sold and y represent the total cost.
Tip: find your equations, either graph or use another method to find your solution.
(4,40)
Lyndsey's rectangular bedroom has a perimeter of 44ft. the Length of her bedroom is 2 feet more than the width. Find the length and width of Lyndsey's bedroom.
Help: Perimeter would be all the sides added together, so you have 2 lengths and 2 widths.
w=10
l=12
Solve the system by graphing
y=-x+2
3x+3y=6
Infinitely Many Solutions
Solve the system using substitution
-5x+6y=12
y=5/6x+2
Infinitely many solutions
Solve the system using elimination
3x-10y=-84
x+5y=47
(2,9)
At a movie theater, 2 medium drinks and a large popcorn costs $13.85. At the same theater, a family bought 3 medium drink s and 2 large popcorns for a total of $23.90.
Write a system of equations to represent the scenario (2 equations).
3x+2y=23.9
2x+y=13.85
Maci put 200 inches of ribbon along the border of a rectangular bulletin board. If the length of the bulletin board is 4 times the width, then what are the dimensions?
Tip: write two equations first to set up your systems
Length: 80in
Width: 20in
Solve the system by graphing
y=2/3x-2
y=-4
(-3,-4)
Solve the system using substitution
y=5/6x+2
6y=5x-12
No Solution
Solve the system using substitution
-3x+2y=48
3x+y=42
(4,30)
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle.
Tip: Supplementary means angles that sum up to 180 degrees.
15 degrees and 165 degrees
Brody went on vacation and purchased postcards and stamps to send letters home while he was away. Two postcards and four stamps cost $3. A postcard cost 4 times as much as a stamp. Set up a system of equations (two different equations).
x=cost for postcard
y=cost for stamp
x=4y
2x+4y=3
Solve the system by graphing
y=1/2x+3
-x+2y=-6
No Solution
Solve the system using substitution
y=-3/2x+9
2x+2y=16
(2,6)
Solve the system using elimination
8x-2y=-6
-3x+y=4
(1,7)
Tickets to an event cost $15 online and $25 at the door. One hundred more people bought their tickets at the door than online. If ticket sales totaled $20,500, write and solve a system to determine the number of people who bought their event tickets online.
450 people
Adam worked two jobs this past summer to start saving for a puppy. He mowed lawns during the day and worked at Pappo's Pizza in the evenings. In one month, Hudson earned a total of $1,400. If he earned $360 more at Pappo's than mowing lawns, how much did he earn at each job?
Mowing: $520
Pappo's Pizza: $880