Conceptual Q's
Easy Problems
Hard Problems
Very Hard Word Problems
100
What is a 2x2 system's of equations?
Two equations, that are solved with elimination or substitution together to solve two variables.
100
x + y = 6
x - y = 2
(4,2)
100
9x + 2y = 30
15x + 8y = 57
(3,1.5)
100
Victoria has 3 pens, red ones cost 2 dollars and black ones cost 1 dollar. She spent 5 dollars on them. How many of each color does she have?
2 red, 1 black.
200
What is elimination?
Using subtraction/addition to cancel out one of the variables.
200
3x+8y=31
x+y = 7
(5,2)
200
2x + 2y = 6
12 = 2y - x
(-2,5)
200
I have 9 apples and oranges in total. Apples cost 3 dollars, and oranges cost 2 dollars. I spent 22 dollars in total. How many of each fruit do I have?
4 apples and 5 oranges. (Those are some pricey fruits)
300
What is substitution?
Isolating a variable in one of the equations and substituting it in the other equation to end up with an equation with only one variable.
300
-2x + 4y = 8
-5x + 8y = 10
(6,5)
300
10x + 7y = 49
10y - x = 70
(0, 7)
300
Victoria purchased 9 bars of candy in total. Each KitKat cost 3 dollars, and every Snickers cost 16 dollars (Super King sized). She spent 105 dollars in total. How many snickers did she buy?
6
400
How do you check you answers?
Substitute your x and y values into your original equations to see if they are correct.
400
12x + 3y = 30
5x + 20y = 50
(2,2)
400
-6x + 2y = 32
-11x + 3y = 50
(-1,13)
400
Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 5 minutes total giving both instructions, and spoke 270 more words in Polish than in Hungarian.
How long did Sakura speak in Hungarian, and how long did she speak in Polish?
2 min in Hungarian, 3 min in Polish
500
How would you find the x and y values of a 2x2 system using a graph?
Graph the lines, and the intercept is the x and y values.
500
4y + 2x = 5
x = 8 - 2y
No Solution!!
500
2x + 2y = 4
5y - 3x = 6
(
,
)
500
A stone falls from the top of a cliff into the ocean.
In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds. How long did the stone fall in the air, and how long in the water?
7 sec in air, 5 sec in water.