Substitution
y = 6x − 11
−2x − 3y = −7
(2,1)
−4x − 2y = −12
4x + 8y = −24
(-18,6)
Find the value of two numbers if their sum is 12 and their difference is 4.
(4, 8)
2x − 3y = −1
y = x − 1
(4,3)
4x + 8y = 20
−4x + 2y = −30
(7, -1)
The difference of two numbers is 3. Their sum is 13. Find the numbers
(8, 5)
y = −3x + 5
5x − 4y = −3
(1,2)
x − y = 11
2x + y = 19
(10, -1)
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
34
−3x − 3y = 3
y = −5x − 17
(-4, 3)
−6x + 5y = 1
6x + 4y = −10
(-1,-1)
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
y = −2
4x − 3y = 18
(3, -2)
−2x − 9y = −25
−4x − 9y = −23
(-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