Elimination 1
-4x-2y=-12
4x+8y=-24
(6,-6)
4x+8y=20
-4x+2y=-30
(7, -1)
x-y=11
2x+y=19
(10, -1)
-6x+5y=1
6x+4y=-10
(-1, -1)
Find the value of two numbers if their sum is 12 and their difference is 4.
4 and 8
-2x-9y=-25
-4x-9y=-23
(-1, 3)
8x+y=-16
-3x+y=-5
(-1, -8)
-6x+6y=6
-6x+3y=-12
(5, 6)
7x+2y=24
8x+2y=30
(6, -9)
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
small box of oranges: $7, large box of oranges: $13
5x+y=9
10x-7y=-18
(1, 4)
-4x+9y=9
x-3y=-6
(9,5)
−3x + 7y = −16
−9x + 5y = 16
(−4, −4)
−7x + y = −19
−2x + 3y = −19
(2, −5)
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
16x − 10y = 10
−8x − 6y = 6
(0, −1)
8x + 14y = 4
−6x − 7y = −10
(4, −2)
−4x − 15y = −17
−x + 5y = −13
(8, −1)
−x − 7y = 14
−4x − 14y = 28
(0, −2)
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
boat: 12 mph, current: 9 mph
−7x − 8y = 9
−4x + 9y = −22
(1, −2)
5x + 4y = −30
3x − 9y = −18
(−6, 0)
−4x − 2y = 14
−10x + 7y = −25
(−1, −5)
3x − 2y = 2
5x − 5y = 10
(−2, −4)
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?
Van: 18, Bus: 59
5x + 4y = −14
3x + 6y = 6
(−6, 4)
2x + 8y = 6
−5x − 20y = −15
Infinite number of solutions
−14 = −20y − 7x
10y + 4 = 2x
(2, 0)
3 + 2x − y = 0
−3 − 7y = 10x
(−1, 1)
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
senior citizen ticket: $4, child ticket: $7