Vocabulary
the definition is: when two or more linear equations are analyzed together.
System linear of Equations
Solve the following system:
y=3x-1
2x+y=9
(2,5)
Solving the following system:
x+3y=-9
-x+y=-7
(3,-4)
Solving the following system:
5x+y=11
x-y=1
(2,1)
The sum of two numbers is 12, and their difference is 6. What are the two numbers?
(3,9)
An ordered pair that states where the two lines intersect. Example: (1,2)
Solution
Solve the following system:
3y-2x=4
x=3-y
(1,2)
Solving the following system:
2x+6y=-12
3x-2y=4
(0,-2)
Solving the following system:
x+y=-1
x-y=3
(1,-2)
The difference of two numbers is 3. Their sum is 13. Find the numbers.
5 and 8.
How many solutions are there when two linear lines have the same slopes and same y-intercepts?
Infinite Solutions (coincident lines)
Solving the following system:
2x-y=-8
3x+2y=-5
(-3,2)
Solving the following system:
−3x + 7y = −16
−9x + 5y = 16
Solving the following system:
y=-3x
x+y=2
(-1,3)
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
How many solutions are there when two linear lines have the same slopes and different y-intercepts?
No solution (parallel lines)
Solving the following system:
3x-6y=30
2y=x+6
No solution
Solving the following system:
5x+2y=2
3x+5y=24
(-2,6)
Solving the following system:
2x-4y=-4
3x-y=4
(2,2)
The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Van: 8, Bus: 22
How many solutions are there when two linear lines have different slopes and different y-intercepts?
One solution
Solving the following system:
3.5x + 2.5y = 17
-1.5x - 7.5y = -33
(2,4)
Solving the following system:
x/2 + y/8 = 4
x/3 - y/2 = -2
(6,8)
Solving the following system:
5x + 4y = −30
3x − 9y = −18
(-6,0)
A girl has $6 in 36 coins (all quarters (0.25) and nickels (0.05). How many of each does she have?
21 quarters, 15 nickels