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Algebra- Graphing - Practice Problems

1. Which of the following graphs correctly describes the system and its solution?
x + 4y = 12
y = -x
A) B)
C) D) None of these.

2. Which of the following systems of equations corresponds to the graph?

A) C)
B) D)

3. Solve the system of linear equations:
4x + 10y = -28
6x + 7y = 6
A) {(-2,-2)}
B) {(1,0)}
C) {(8,-6)}
D) ∅

4. Determine if the following system of equations is independent, dependent, or inconsistent:
-7x - 5y = -4
-35x - 25y = 13
A) Independent
B) Dependent
C) Inconsistent

5. Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She averaged 75 mph along the route from Albuquerque to Roswell and averaged 70 mph from Roswell to Carlsbad. She covered the entire 220 miles in 3 hours. How long did she take to drive from Albuquerque to Roswell?
A) 2 hours
B) 1 hour
C) 1.5 hours
D) 2.5 hours

6. Solve the system of linear equations.

A) {(1, 5)}
B) {(3, 7)}
C) {(-3, -6)}
D) No solution. The system is inconsistent.

7. Janet invested $27,000, part at 15% and part at 9%. If the total interest at the end of the year is $3,390, how much did she invest at 15%?
A) $15,000
B) $11,000
C) $17,000
D) $16,000

8. A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. If x is the number of doll houses and y is the number of furniture sets, which system of inequalities given below represents this situation?
A) 3x + 8y ≤ 400
x + y ≤ 100
x ≥ 20
y ≥ 10 C) 400x + 8y ≤ 400
x + 100y ≤ 100
x ≥ 20
y ≥ 10
B) 8x + 3y ≤ 400
x - y ≥ 100
x ≥ 20
y ≥ 10 D) 3x + 8y ≥ 400
x + y ≥ 100
x ≤ 20
y ≤ 10

9. A rectangular corral has a perimeter of 64 yards. Its length is 8 yards more than its width. What are the dimensions of the corral? Find the length and width of the corral. Enter your answers in the blanks. Enter only the numeric values rounded to the nearest tenth.
Length = ________yds Width = _________yds

10. Audrey has a combined total of 35 dimes and quarters in her piggy bank with a total value of $6.95. How many of the coins are dimes and how many are quarters? Enter your answers, as whole numbers, in the blanks.
Dimes = ________ Quarters = ________

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