Verifying/Number of Solutions
Is (0,-4) the solution to the following system?
y = -20x + 1
20x + y = 6
No!
Solve by substitution: (answer as coordinate)
x + y = 2
y = 3
(-1,3)
Solve by elimination: (answer as coordinate)
x + 5y = 12
-x +y = 0
(2,2)
Find the value of two numbers if their sum is 12 and their difference is 4.
8 and 4
True or False:
The factors of x2 + 64 are (x + 8) and (x - 8)
FALSE
Is (-2,1) a solution to the following system?
6x - 3y = -15
2x + y = -3
Yes!
Solve by substitution: (answer as coordinate)
y = 6x - 11
-2x - 3y = -7
(2,1)
Solve by elimination: (answer as coordinate)
-4x - 2y = -12
4x + 8y = -24
(6,-6)
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
Factor:
16x2 - 25
(4x + 5)(4x - 5)
How many solutions are in this linear system?
-x + y = 8
y = -x + 8
ONE SOLUTION
Solve by substitution: (answer as coordinate)
x = -3y +1
4x + 2y = 14
(4,-1)
Solve by elimination: (answer as coordinate)
5x + y = 9
10x - 7y = -18
(1,4)
A jar consisting of only nickels and dimes contains 58 coins. If the total value of coins inside the jar is $4.20, how many of each coin is in the jar?
(Please write your answer as __ nickels and __ dimes)
32 nickels and 26 dimes
Which of the following is NOT a factor of 20x2 - 20y2?
a) 20
b) (2x - 2y)
c) (x + y)
d) (x - y)
B
How many solutions are in this linear system?
2x - 5 = 25
-6x + 15y = 30
ZERO SOLUTIONS
Solve by substitution: (answer as coordinate)
-5x = 8y + 17
2x - 7y = -17
(-5,1)
Solve by elimination: (answer as coordinate)
-4x + 9y = 9
x = 3y - 6
(9,5)
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
Factor:
20x2 - 20y2
20(x + y)(x - y)
If the following system had infinite solutions, what would be the value of k?
3y = 2x - 9
12x - ky = 54
18
Solve by substitution:
-5x + 5y = 10
-x + y = 3
No Solutions
Solve by elimination:
4x + 16y = 12
-10x - 40y = -30
Infinite Solutions
Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
98 small cups and 57 large cups
Factor:
x16 - 1
(x4+1)(x2+1)(x+1)(x-1)