Vocabulary
What is this form called?
Ax + By = C
Standardform
When two points meet on a graph it is called an ____________________.
Intersection
True or false: You can eliminate s without having to multiply the equations by anything.
r + s = -6
r - s = -10
True
What is the first step to set up this problem?
x = 4y
2x + 3y = 22
The sum (total) of two numbers is 104. How could you write this as an equation?
x + y = 104
The answer to an equation or system of equations is the called the ___________.
solution
The solution to the system of equations:
y = 3x - 2
y = -x - 2
What is (0, -2)?
What could you multiply the bottom row by to eliminate a?
8a + 5b = 9
2a - 4b = -4
-4
What is the first step to solve this problem?
y = x - 2
3x - y = 16
3x - x -2 = 16
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660.
How do you set up the equations to solve this problem?
6s + 8h = 700
9s + 6h = 660
The form y = mx+ b is called _______________.
y = -3
x = 5
What could you multiply the top and bottom rows by to eliminate x?
2x + 3y = 6
3x + 5y = 15
- 3 and 2
OR
3 and -2
What is the first step to solve this problem?
y = 3x - 1
7x + 2y = 37
7x + 2(3x-1) = 37
To sign up for track, it costs each player $15 plus a registration fee for the team of $400. To sign up for volleyball, it costs each player $10 plus a registration fee of $550 for the team.
Write a system of equations to solve the problem.
y = 15x + 400
y= 10x + 550
15x + 400 = 10x + 550
When you replace the value of one variable (letter) in another equation, this is called
Substitution
y = (1/3)x - 3
2x - y = 8
The solution to the system:
-4x - 2y = -12
4x + 8y = -24
(6, -6)
The solution to the system:
y= x + 5
3x + y = 25
(5, 10)
Tickets to a soccer game cost $5.00 if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
How could you set up the equations to solve this problem?
5b + 7.5g = 3500
b + g = 600
When you get rid of a variable (letter) by adding the two equations, this is called _______________.
Elimination
The solution to the system of equations:
y = 8x
-x + 6y = 0
(0,0)
x - y = 11
2x + y = 19
(10, -1)
The solution to the system
y = 6x-11
-2x - 3y = -7
(2, 1)
At a theater, youth tickets to the movies are $5 and adult tickets are $10. One night, the movie theater had 440 people attend their movies. They sold a total of $2800 in tickets.
Write a system of equations to set up this problem.
5s + 10a = 2800
s + a = 440