Systems by Numbers
Solve the following using substitution:
7x + 8y = 0
y = -6x
What is (0,0)
Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each type of coin does he have?
17 Nickels and 32 Quarters
Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $270 on 6 new shirts and 18 pairs of shorts. The older brother purchased 6 new shirts and 14 pairs of shorts and paid a total of $222. How much did each item cost?
Shirts cost $9 shorts cost $12
y = −8
y = −2x − 12
What is (-2, -8)
A tennis coach took his team out for lunch and bought 8 hamburgers and 5 fries for $24. The players were still hungry so the coach bought 6 more hamburgers and 2 more fries for $16.60. Find the cost for one hamburger.
2.50
The owner of two hotels is ordering towels. He bought 65 hand towels and 24 bath towels for his hotel in Hampton, spending a total of $517. He also ordered 65 hand towels and 49 bath towels for his hotel in Manchester, spending $717. How much does each towel cost?
Hand towels cost $5 Bath towels cost $8
2x + 5y = 17
y = 3x
What is (1,3)
Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy?
14
An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 small baskets and 4 large baskets, using a total of 84 pieces of fruit. Using wire baskets, the employee assembled 4 small baskets and 4 large baskets, using a total of 100 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
Small baskets have 8 pieces of fruit. Large baskets have 17 pieces of fruit
y = 2x − 15
y = 2x+4
What is No Solution?
Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart.
During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak
sandwiches did he sell?
634
The Somerville High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Moran has requested 85 earth science textbooks and 79 physics textbooks for all of her classes, which costs the department a total of $9,185. Mr. Melton has asked for 85 earth science textbooks and 74 physics textbooks, which will cost a total of $8,835. How much do the textbooks cost?
Physics textbooks cost $70 Earth science textbooks cost $43
y= 14x -10
-14x +y = -10
What is Infinite Solutions?
Steven has a collection of nickels and dimes. In all, he has 17 coins. The total value of the collection is $1.15.
How many nickels does he have?
What is 11?
Mr. Bryant is the volunteer coordinator for a company that puts on running races. Last year, the company organized 10 short races and 9 long races, which required a total of 804 volunteers. This year, the company organized 10 short races and 6 long races, which required 636 volunteers in total. How many volunteers does each type of race require?
Short races need 30 volunteers Long races need 56 volunteers