The first question revolves around finding the solution of a system of equations. Make sure to answer what the question is asking for.
Q1.
x+3y = 2
4x-3y = 23
The given system of equations has a solution (x, y). What is the value of 4x?
A. -5
B. 7
C. 5
D. 20
Answer: D
Explanation: The correct answer is 25. For this system of equations, you can eliminate the y-terms by adding both equations. The resulting equation is 5x = 25. Dividing both sides by 5 yields x = 5. Finally, multiplying x by 4 yields 20.
The second question is an application using system of equations. Be sure to read the problem and write your two equations for the system of equations.
Q2.
Ashanti has been acting for x years, and Diana has been acting for d years. If Ashanti has been acting for 1.5 times as long as Diana has, which is also 4 years longer than Diana has been acting, which of the following system of equations correctly models this situation?
A. x = 1.5d
x = d + 4
B. x = 1.5d
d = x + 4
C. d = 1.5a
d = x + 4
D. d = 1.5a
d = x + 4
Answer: A
Explanation: To model this example, we need to remember that x is the variable that represents the number of years that Ashanti has been acting, while d represent the number of years Diana has been acting. Since the number of years Ashanti has acted is 1.5 times the number of years Diana acted, x = 1.5d. Additionally, since Ashanti has also acted 4 years longer than Diana, x = d + 4. Therefore, A is correct.