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### Student Question

How to solve this with the comparison method:

y = 3x + 2

y = 5x-24

Mathematics ## Explanations (1)

• Explanation from Alloprof  Explanation from Alloprof

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

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