MHB Finding the Point of Intersection: Is (-2, -2.5) the Solution?

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To find the point of intersection of the lines represented by the equations 4y = x - 8 and 2y = 3x + 1, simultaneous equations can be solved using substitution or elimination. By rewriting the second equation as 4y = 6x + 2, both equations can be set equal to each other. Solving the resulting equation x - 8 = 6x + 2 yields x = -2. Substituting x = -2 back into either equation confirms that y = -2.5, establishing that the point of intersection is indeed (-2, -2.5).
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Hi,

I am looking for some help on how you find the point of intersection of the following two lines:

4y = x - 8
2y = 3x + 1

Thanks for any help.

/Nichola
 
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nicholar1 said:
Hi,

I am looking for some help on how you find the point of intersection of the following two lines:

4y = x - 8
2y = 3x + 1

Thanks for any help.

/Nichola

Hi Nichola

The intersection will be at the point where the equations are equal. Are you familiar with solving simultaneous equations either by substitution or elimination?

Multiply the second equation by 2:

[math]4y = 6x+2[/math]

You can then subtract this equation from the first one to eliminate y
 
SuperSonic4 said:
Hi Nichola

The intersection will be at the point where the equations are equal. Are you familiar with solving simultaneous equations either by substitution or elimination?

Multiply the second equation by 2:

[math]4y = 6x+2[/math]

You can then subtract this equation from the first one to eliminate y

Hi,

No I have never done simultaneous equations before, that's where I'm getting confused, how they work together.
 
nicholar1 said:
Hi,

I am looking for some help on how you find the point of intersection of the following two lines:

4y = x - 8
2y = 3x + 1

Thanks for any help.

/Nichola

nicholar1 said:
Hi,

No I have never done simultaneous equations before, that's where I'm getting confused, how they work together.

Welcome to MHB Nichola! :)

We can multiply the second equation by 2 as Supersonic suggested.
That is, we start with:
$$2y = 3x + 1$$
and we end up with
$$4y = 6x + 2$$

Now we can see that according to the first equation $4y=x-8$ and according to the rewritten second equation we also have that $4y=6x+2$.
Since both are equal to $4y$ it must be that $x-8$ is equal to $6x+2$.

How would you solve the equation $x-8 = 6x+2$?
 
I like Serena said:
Welcome to MHB Nichola! :)

We can multiply the second equation by 2 as Supersonic suggested.
That is, we start with:
$$2y = 3x + 1$$
and we end up with
$$4y = 6x + 2$$

Now we can see that according to the first equation $4y=x-8$ and according to the rewritten second equation we also have that $4y=6x+2$.
Since both are equal to $4y$ it must be that $x-8$ is equal to $6x+2$.

How would you solve the equation $x-8 = 6x+2$?

So to solve the equation $x-8 = 6x+2$ we:

Add 8 to both sides: $x = 6x+10$
Subtract 6x from both sides: $-5x = 10$
Divide both sides by -5: $x = -2$

So, substituting x = -2 into the equations give:

$4y = -2 - 8 = -10$

$2y = 3 x (-2) + 1 = -5$

So dividing -10 by 4 or -5 by 2 gives -2.5.

So does that mean the point of intersection is (-2, -2.5)?

Thanks for the help guys :)

/Nichola
 
nicholar1 said:
So to solve the equation $x-8 = 6x+2$ we:

Add 8 to both sides: $x = 6x+10$
Subtract 6x from both sides: $-5x = 10$
Divide both sides by -5: $x = -2$

So, substituting x = -2 into the equations give:

$4y = -2 - 8 = -10$

$2y = 3 x (-2) + 1 = -5$

So dividing -10 by 4 or -5 by 2 gives -2.5.

So does that mean the point of intersection is (-2, -2.5)?

Thanks for the help guys :)

/Nichola

Let's verify...

Substiting (-2, -2.5) in:
\begin{aligned}4y &= x - 8 \\
2y &= 3x + 1
\end{aligned}
gives:
\begin{aligned}4 \cdot -2.5 &= -2 -8 \\
2 \cdot -2.5 &= 3 \cdot -2 + 1
\end{aligned}
simplifying:
\begin{aligned}-10 &= -10 \\
-5 &= -5
\end{aligned}

We have a match, so this is the correct solution! (Happy)
 
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