systems
of
equations
are
sweet
100
x - y = 1 x + y = 3
(2,1)
100
3c - d = -1 -3c - d = 5
(-1, -2)
100
4x + y = 23 3x - y = 12
(5, 3)
100
y = 6x 2x + 3y = -20
(-1, -6)
100
x + 2y = 3 x + y = 1
(-1, 2)
200
-x + 3y = 6 x + 3y = 18
(6, 4)
200
x - y = 4 2x + y = -4
(0, -4)
200
5x + 2y = 7 -2x + 2y = -14
(3, -4)
200
x = -4y 3x + 2y = 20
(8, -2)
200
the length of Sally's garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. what are the dimensions of Sally's garden?
28 meters by 8 meters
300
x + 4y = -8 x - 4y = -8
(-8, 0)
300
3x + 2y = -19 -3x - 5y = 25
(-5, -2)
300
2x - 6y = 6 2x + 3y = 24
(9, 2)
300
3x + y = 12 y = -x - 2
(7, -9)
300
Two-tenths of a number plus another number is seven-tenths. Two-tenths the first number plus twice the second number is 1.2. What are the two numbers?
(1, 0.5)
400
5x - y = -6 -x + y = 2
(-1, 1)
400
3x + 2y = -1 4x + 2y = -6
(-5, 7)
400
four times one number added to another number is 36. Three times the first number minus the other number is 20. What are the two numbers?
8 and 4
400
4x - 5y = -7 y = 5x
(.33333333333..., 1.666666666666666...)
400
The chess club has 16 members and gains a new member every month. The film club has 4 members and gains 4 new members every month. Write and solve a system of equations to find when the number of members in both clubs will be equal.
4 months
500
find the two numbers whose sum is 54 and difference is 4
(25, 29)
500
2.5x + y = 10.7 2.5x + 2y = 12.9
(3.4, 2.2)
500
Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. How many adult tickets and how many student tickets were purchased.
5 adult and 3 student
500
The Texas State Legislature is made up of senators and representatives. The sum of the number of senators and representatives is 181. There are 119 more representatives than senators. How many senators and how many representatives are in the Texas State Legislature?
31 senators and 150 reps.
500
English is spoken as the first or primary language in 78 more countries than Farsi is spoken as the first language. Together, English and Farsi are spoken as a first language in 130 countries. In how many countries is English spoken as a first language? In how many countries is Farsi spoken as the first language?
English: 104 countries Farsi: 26 countries
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