Substitution
y = 4x − 3
3x + 2y = 16
(2,5)
5x + 3y = 31
−5x + 4y = 18
(2,7)
The sum of two numbers is 22. Their difference is 6. Find the numbers.
(14,8)
x = 7y − 10
4x + 5y = −7
(-3,1)
2x − y = 15
5x − y = 24
(3, -9)
A collection of $5-bills and $20-bills has a total value of $345 and contains 30 bills. How many $5-bills and how many $20-bills are in the collection?
(17,13)
y = 2x − 16
y = 3x − 22
(6, -4)
3x + 2y = 18
7x − 4y = 16
(4,3)
A baseball game has tickets for sale. Student tickets cost $4.25 each and adult tickets cost $7.75 each. If 100 tickets were sold for a total of $530, how many of each type were sold?
(70,30)
2y = 4x + 20
4x + 7y = 70
(0,10)
4x + 2y = −52
7x − 3y = −39
(-9,-8)
James invested $25,000. Part of the money was invested at 6% per year and the remainder was invested at 8% per year. If James profited $1,760 at the end of the first year from both investments combined, how much did he invest at each rate?
(12,000, 13,000)
x − 3y = −2
4x = 12y − 8
ARN
2x + 4y = 10
3x + 6y = 15
ARN
For a fundraiser, the choir is selling bags of popcorn and boxes of chocolate covered pretzels. Mr. Cotterman bought 5 bags of popcorn and 3 boxes of chocolate covered pretzels for $85. Mrs. Seidel bought 4 bags of popcorn and 2 boxes of chocolate covered pretzels for $62. What is the price for each item?
(8,15)