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# Help Zone

### Student Question

Hello!

I have two lines

1) y = 5x-33

2) 15-2y = x

How do I find the point where they intersect?

Mathematics ## 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 • 1yr. edited September 2021

Hello Fast Fox!

To find the point of intersection between the 2 lines you can use the comparison method!

I'll explain how to do it!

First, you need to express the two equations in terms of the same variable. It is more obvious to express them in terms of x.

You will therefore have to find the shape of the second line to have y = mx + b.

To do this you have to isolate y.

Then you will compare the two functions by setting that y1 = y2, like that:

$$y1 = y2 \Rightarrow 5x − 33 = \frac {-x}{2} + 7.5$$

As there is only one variable left (the x), you can isolate it to find the x coordinate of the crossing point!

When the value of x is known, you can replace it in one of the two equations to find the value of y.

You can then put the point in the form (x, y)