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Secondary III • 9mo.

How to solve this with the comparison method:

y = 3x + 2

y = 5x-24

Mathematics
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Explanations (1)

  • Explanation from Alloprof

    Explanation from Alloprof

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

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    Team Alloprof • 9mo.

    Hi!

    I'm not going to solve it for you, but what I suggest is that I do a detailed example of how to use this method. You can then apply it on your own to solve that problem.

    Let's try to solve this:

    $$y+3x=5 \: \:\: and \:\:\: y= 2x+9$$

    1. First, you have to isolate the same variable in your two equations. Let's isolate y (you could have isolated x too)

    $$y=5-3x \: \: \: and \: \:\: y= 2x+9$$

    2. Second, we want to have a single variable in an equation. We will set y = y

     $$y=y$$


    $$Therefore, \: 5-3x = 2x+9$$


    3. Third, we must find the variable x by isolating it.

    $$5-3x = 2x+9$$


    $$5-9 = 2x+3x$$


    $$-4= 5x$$


    $$\frac{-4}{5}=x$$

    4. Finally, replace the result of x in one of our two initial equations. We can also replace it in both the equations if we want to verify our answer. Indeed, the result of y should be the same whether you replace the x in the first or in the second equation.

    $$y= 2x+9$$


    $$y= 2\frac{-4}{5}+9$$


    $$y= 2\frac{-4}{5}+9$$


    $$y= \frac{37}{5}$$

    Hope this helped you. If you have other questions, do not hesitate.

    Have a nice day!

    KH