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Math 10 Pre IB
Assignment #1A: Systems of Equations
NAME:__________________
1. Solve each of the following systems by the method indicated. Show all work! (8 pts)
(a)
x y 7
3 x  4 y  24
(graphing)
10
(b)
x  2 y  13
2 x  3 y  9
(substitution)
y
8
6
4
2
−10 −8 −6 −4 −2
−2
x
2
4
6
8
10
−4
−6
−8
−10
(c)
7x  3y  9
5x  2 y  7
(elimination)
x y
 2
3 2
(d)
(any method)
5
3
x  y 1
6
4
2. Given the equation  2 x  y  4 , write another linear equation that will form a linear system with:
(3 pts)
(a) Exactly one solution
(b) No solution
(c) infinite solutions
3. Solve each of the following problems algebraically. Identify all variables and show all work! (9 pts)
(a) In a piggy bank there are dimes and quarters for a total of $9.60. If there are twice as many quarters
as there are dimes, find the number of each type of coin.
(b) A farmer only has hens and pigs in an enclosure. He said to his daughter Susan, “You know we only
have hens and pigs. I counted 48 heads altogether and 122 legs. Can you tell me how many of each
animal type we have?” It was too dark for Susan to go out and count them, but she thought for awhile
and gave the correct answer. What answer did she obtain and how did she do it?
(c) The last digit of a three-digit number is a 4. The sum of the digits is 18. When you reverse the first
two digits, the number decreases in value by 180. What is the number?
Math 10 Pre IB
Assignment #1B: Systems of Equations
NAME:__________________
1. Solve each of the following systems by the method indicated. Show all work! (16 pts)
(a)
x  2 y  4
2 x  y  5
(graphing)
10
(b)
x  3y  7
2 x  5 y  13
y
8
6
4
2
−10 −8 −6 −4 −2
−2
x
2
4
6
8
10
−4
−6
−8
−10
(c)
2x  3 y  6
5 x  10 y  20
(elimination)
1
2
x  y 1
2
3
(d)
1
1
5
x y 
4
3
2
(substitution)
2. Given the equation  6 x  y  3 , write another linear equation that will form a linear system with:
(3 pts)
(a) Exactly one solution
(b) No solution
(c) infinite solutions
3. Solve each of the following problems algebraically. Identify all variables and show all work! (9 pts)
(a) In a piggy bank there are dimes and quarters for a total of $12.15. If there are twice as many dimes as
there are quarters, find the number of each type of coin.
(b) A farmer only has hens and pigs in an enclosure. He said to his daughter Susan, “You know we only
have hens and pigs. I counted 46 heads altogether and 130 legs. Can you tell me how many of each
animal type we have?” It was too dark for Susan to go out and count them, but she thought for awhile
and gave the correct answer. What answer did she obtain and how did she do it?
(c) The last digit of a three-digit number is a 7. The sum of the digits is 15. When you reverse the first
two digits, the number increases in value by 180. What is the number?