Number of Solutions
How many solutions would a set of parallel lines have?
No solutions
3x - y = 34
7x + 2y = 132
y (y = 3x-34)
Solve using elimination.
6𝑥−5𝑦=8
−12𝑥+2𝑦=0
𝑥=−1/3, 𝑦=−2
At Chipotle, your friend orders two orders of chips and two orders of guac for $12. Someone else in line orders one order of chips and three orders of guac (they really like guac) for $15.
What system of equations could we use to represent this problem?
2x + 2y = 12
x + 3y = 15
What was the original name of the Town of Arlington? (it was an Algonquin word for "swift running water")
Menotomy
Does this system of equations have one solution, no solutions, or infinitely many solutions?
3x + 2y = 15
9x + 6y = 45
Infinitely many solutions
Solve this system using substitution.
𝑥 + 2𝑦 = 15
𝑥 - 3𝑦 = −25
x = -1, y = 8
Solve using elimination.
-3x+4y=39
7x-5y=0
x=15
y=21
Ten turtles and three tigers collectively weigh 200 pounds.
Six turtles and two tigers collectively weight 130 pounds.
Assuming all the turtles each weigh the same and all the tigers each weigh the same: How much does a single turtle weigh?
5 pounds
What country has won the most (football/soccer) World Cup titles throughout history?
Brazil
Does this system of equations have one solution, no solutions, or infinitely many solutions?
4x + 3y = 24
3x + 5y = 13
One solution
Solve this system using substitution.
𝑥−𝑦=−10
8𝑥+(1/2)𝑦=−12
𝑥=-2, y=8
Solve using elimination.
2𝑥+3𝑦=20
7𝑥+2𝑦=53
x=7, y=2
Mr. Bristol gave a test. One student 92 points for getting eight multiple choice problems correct and four open response problems correct. Another student earned 81 points for getting ten multiple choice problems correct and three open response problems correct.
How much were open response problems worth?
17 points.
What musical artist created the most streamed song of all time?
The Weeknd
Does this system of equations have one solution, no solutions, or infinitely many solutions?
x = 4
y = -6
One solution
Solve using substitution.
7𝑥−8𝑦=−12
−4𝑥+2𝑦=3
𝑥=0,𝑦=3/2 or y=1.5
5x + 13y = 232
12x + 7y = 218
What constant should each equation be multiplied by to eliminiate x?
First eq: 12 or -12
Second eq: 5 or -5
A rectangle has a perimeter of 44 inches and an area of 72 square inches.
What is the length and width of the sides of this rectangle?
width = 4 in, length = 18 in
Ben-Hur (1959)
Titanic (1997)
The Lord of the Rings: Return of the King (2003)
Does this system of equations have one solution, no solutions, or infinitely many solutions?
5x - 3y = -15
-5x + 3y = 23
No solution
Solve using substitution.
3𝑥+9𝑦=−6
−4𝑥−12𝑦=8
There are infinitely many solutions.
Solve using elimination.
−2𝑥+50𝑦=25
𝑥−25𝑦=3
These equations have no solution.
A boat traveled 336 miles downstream (with the current) and 336 miles back (against the current). The trip downstream took 12 hours. The trip back took 14 hours.
What is the speed of the boat in still water? What is the speed of the current?
speed of boat - 26mph, current - 2mph
What language does the English word "algebra" originate from? (roughly translates to "restoration")
Arabic - al-jabr الجبر