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Question 1
9x + 2y = -61 …………. (1)
X = 1 – 8y …………… (2)
Answer:
Substitute value of x in equation 1 , we get
9(1 – 8y) + 2y = -61
- 9 – 72y +2y = -61
- Y = 70/70 = 1
Substitute value of y in x , we get x = 1 - 8 = -7
Solution is (-7,1).
Question 2
Determine whether (-5,2) is a solution of 5x-9y=4
Answer:
Put (-5, 2) in 5x – 9y = 4
We get 5*(-5) – 9*2 = -25 – 18 = -43 which is not equal to 4 thus it is NOT a solution of this problem.
Question 3
Translate to an algebraic expression. The product of 36 percentages and some number
Answer:
Let x be any some number and 36% of this number = 36x/100 = 0.36x
Question 4
Use the distributive property to solve the following questions
5(w-2) = -10
Answer:
5(w - 2) = 10
=> 5w – 10 = 10 => 5w = 20 => w = 4
Question 5
simply
9(32 – (56 - 33))
Answer:
9(32 – (56 - 33)) = 9(32 – 23 ) = 9*9 = 81
Question 6
Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 84 miles per hour. Train A passes a station at 7:25 PM. If tran B passes the same station at 7:55 PM. At what time train B catch up to train A?
Answer:
Let x be the distance travelled by the train from the station
Since Train A start its journy ½ hr before the train B start its journey.
Suppose after t hrs both trains will meet . Thus x = 80 (t + 1/2)
X = 84(t)
From both equations, 80t + 40 = 84t
- 4t = 40 => t = 10 hrs
- Thus after 10 hrs both trains will meet.
Question 7
Graph the following equations
Y >= -3
x>= 5
Answer:
Question 8
5x/8 + x/16 = 3/16 + x
Answer:
11x/16 – x = 3/16
-5x/16 = 3/16
x = -3/5
Question 9
-18 <= 4x – 7
Answer:
-18 + 7 <= 4x
-11 <= 4x => -11/4 <= x
And
4x – 7 <= -6
4x <= -6 + 7
4x <= 1
X <= ¼
Thus -11/4 <= x <= ¼
