Vocab
A set of two or more equations that use the same variable
System of Equations
Find the additive inverse of 4
-4
2X+3y=10 and X-2y=4
(32/7, 2/7)
3X + 2y= 10 and 2X-Y = 5
(3, 1/2)
You have 10 coins which add up to $2.50. You have quarters and dimes. How many of each do you have?
10 quarters, 0 dimes
When the graph of each equation of a system is a line
System of Linear Equations
Find the additive inverse of 2X
-2X
3x−2y=5 and 2X+4y=14
(3, 2)
4X-3Y=7 and 2X + 5Y=11
(34/13, 15/13)
You sell T-shirts for $25 a piece. Your cost to produce shirts include a $10 initial fee and a $5 for making the shirt. What is the minimum you would need to sell to break even?
at least 1 shirt
A type of system of equations in which two lines never intersect
Inconsistent
Find the multiplicative inverse of 3X
1/3X
X+Y = 8 and 3X-2Y= 4
(4,4)
2X + Y = 5 and 3X-2Y= 4
(2, 1)
You are building a dog park fence. The length is 3 times more than the width, which is 15 feet. What is the area of the dog park?
675 square feet
Using the additive property of equality or the additive inverse to modify or cancel a variable, this process is called what?
2X-4= 10
X = 7
2X-Y=1 and 3X + Y = 9
(2, 3)
3X- 4Y = 2 and 5X + 2Y = 7
(16, 13)
You have a total of 600 votes for the student prom queen. The number of juniors who cast a vote is 10 times more than the number of seniors. How many votes were cast per each grade? Round to the nearest whole number.
545 juniors, 55 seniors
When the slopes and y values are the same, this system is called?
Dependent
3(x-5) = 18
x=11
3X-2Y = 5 and 4X + 3Y = 14
(2.529, 1.294)
2X + 3Y = 11 and 4X - 5Y = 3
(32/11, 19/11)
Joey bought 3 types of books: Science Fiction, Fantasy and Mystery. The fantasy books cost $2.50, the science fiction cost $3.50 and the Mystery books cost $5. If she has $20 to spend and wants to buy a total of 6 books, how many can she buy of each genre?
5 science fiction, 1 fantasy and 0 mystery books