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Graphing Systems
Systems by Substitution
Systems by Elimination
Word Problems: Substitution
Word Problems: Elimination
100
Find the solution for: y= -7x -3 y= 4
What is (-1, 4)
100
Solve the following using substitution: 7x + 8y = 0 y = -6x
What is (0,0)
100
4x + 8y = 20 −4x + 2y = −30
What is (7, -1)
100
At a yoga studio, one option is to buy a membership that is $84 a month for unlimited classes. The other option is to pay $7 per class. At what point will both memberships cost the same amount?
For both options, 12 classes will cost you $84
100
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 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
200
y = 1/3x - 4 y = -7/3x +4
What is (3, -3)
200
y = −8 y = −2x − 12
What is (-2, -8)
200
8x + 2y = 30 7x + 2y = 24
What is (6, -9)
200
Mei is going to ship some gifts to family members, and she is considering two shipping companies. The first shipping company charges a fee of $10 to ship a medium box, plus an additional $6 per kilogram. A second shipping company charges $22 for the same size of box, plus an additional $3 per kilogram. At a certain weight, the two shipping methods will cost the same amount. How much will it cost? What is that weight?
At both companies, 4 kg will cost $34
200
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
300
y = -6x -3 y= -x +2
What is (-1,3)
300
2x + 5y = 17 y = 3x
What is (1,3)
300
−6x + 6y = 6 −6x + 3y = −12
What is (5,6)
300
Braden and Grayson each opened a savings account on the same day. Braden started by putting $294 in his account, and he will deposit an additional $239 each week. Grayson made an initial deposit of $315, and he will add $232 more each week. Eventually, Braden and Grayson will each have the same amount saved. What is that amount? How many weeks will that take?
Braden and Grayson will each have saved a total of $1011 after 3 weeks
300
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
400
-3y − 3x = 9 -3x + y = 1
(-1, -2)
400
y = 2x − 15 y = 5x
What is (-5, -25)
400
8x + 14y = 4 6x + 7y = 10
What is (4, -2)
400
A boy scout troop is selling Christmas trees at a local tree lot. In the morning, they sold 12 Douglas Fir trees and 24 Noble Fir trees, earning a total of $2,352. In the afternoon, they sold 1 Noble Fir tree, earning a total of $75. How much does each type of tree cost?
Douglas Fir trees cost $46 Noble Fir trees cost $75
400
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
500
Sorry, this is not an option. Pick again!
500
y= 14x -10 y= 11x + 2
What is (4, 46)
500
5x + y = 9 -10x + 7y = 18
What is (1, 4)
500
In a paint factory, an old conveyer line has filled 15 barrels of paint, and is filling more at a rate of 6 barrels per minute. A worker just switched on a newer line that can fill 9 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled? How long will that take?
After 5 minutes, both lines will have filled 45 barrels.
500
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