Question

Elimination was used to solve a system of equations.
One of the intermediate steps led to the equation 9x = 27.
Which of the following systems could have led to this equation?
O
9x + 2y = 21
-9x – 2y = 21
10x – y = 15
x+y = – 12
7x – 2y = 15
x + y = 6
4x + 3y = 24
-5x – 3y = 3

Answers

  1. The system of equation that could have led to the equation 9x = 27 is
    7x – 2y = 15
    x + y = 6
    The correct option is the third option
    7x – 2y = 15
    x + y = 6

    Solving systems of equations

    From the question, we are to determine the system that could have led to 9x = 27
    1.
    9x + 2y = 21
    -9x – 2y = 21
    Subtracting, we get
    9x + 2y = 21
    -9x – 2y = 21
    ——————-
    18x + 4y = 0
    2.
    10x – y = 15
    x + y = – 12
    Subtracting, we get
    10x – y = 15
    x + y = – 12
    ———————
    9x -2y = 27
    3.
    7x – 2y = 15
    x + y = 6
    Here, multiply the second equation by 2
    2 × [x + y = 6]
    2x + 2y = 12
    Now, add to the first equation
    7x – 2y = 15
    2x + 2y = 12
    ——————
    9x = 27
    4.
    4x + 3y = 24
    -5x – 3y = 3
    Subtracting, we get
    4x + 3y = 24
    -5x – 3y = 3
    ———————
    9x + 6y = 21
    Hence, the system of equation that could have led to the equation 9x = 27 is
    7x – 2y = 15
    x + y = 6
    The correct option is the third option
    7x – 2y = 15
    x + y = 6
    Learn more on Systems of equations here: https://brainly.com/question/12691830
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