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Student Question

Secondary III • 1yr.

Hello! Sorry to bother you again, but I still don't understand this problem.

I have to do the comparison method with these two equations:

1 → 3x - y = 18

2 ⇾ -2y = -6x - 120

And when I isolated y, it gave me: 

1 → y = 3x + 60

2 → y = 3x - 18

But it doesn't work !!! I came to an unrealistic answer. Can you help me isolate my equations, because I think I made a mistake please. It would help me enormously! Thanks in advance!


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Explanations (1)

  • Explanation from Alloprof

    Explanation from Alloprof

    This Explanation was submitted by a member of the Alloprof team.

    Team Alloprof • 1yr.


    Thank you for calling on our services: D

    Here are the steps of the comparison method:

    1. In the case of a written problem, define the variables and translate the situation into a system of equations.
    2. Isolate the same variable in both equations, if necessary.
    3. Form a one-variable equation by comparing the two algebraic expressions.
    4. Solve this equation
    5. Replace the value found in step 4 in one of the starting equations to find the value of the second variable.
    6. Validate the result by substituting the values ​​obtained for the variables in each of the initial equations.

    Let's do your number together! To begin with, you have well isolated the variable y. The next step is to compare the two equations! So, 3x + 60 = 3x - 18.

    As you said, the result doesn't make sense, because 3x-3x = 0. On the other hand, you get a result. The result means that there is no common point between the two lines. These are therefore parallel.

    By looking at the two equations, we can understand why! They have the same slope and will therefore increase at the same rate. On the other hand, they do not have the same y-intercept. Thus, they will never intersect ;)

    I invite you to visit our Alloprof sheet on the different results of straight line comparisons:

    Pssssst! If you want to practice, here are exercises on the same subject:

    Hope this enlightens you! Do not hesitate if you have other questions, it will be a real pleasure for me to help you again :D