## Linear equations using addition

I'm probably making a silly mistake or Wolfram Alpha is lying to me.

Question: Find the value of c and d.

$3d=13-2c$

$\frac{3c+d}{2}=8$

Rearranged, simplified and multiply each equation by 2:

$$6d+4c=26$$
$$d+3c=16$$

Now find the common multiple which in my case I will use 12:

$$18d+12c=78$$
$$-4d-12c=-64$$

Then add them and find what d is worth:

$$14d=14$$

$$d=1$$

Now when I plug this back into the equation, I will use the first one:

$$3(1)+2c=13$$
$$3+2(c)=13$$
$$c=5$$

$$d=1, c=5$$

What am I doing wrong? Sorry if this is the long winded way to do it.
 Blog Entries: 1 Recognitions: Gold Member Homework Help Science Advisor Your answer is correct, as you can verify by plugging ##d = 1## and ##c = 5## into the two given equations.

 Quote by jbunniii Your answer is correct, as you can verify by plugging ##d = 1## and ##c = 5## into the two given equations.
So Wolfram is lying to me it seems?

Wolfram says the answer is $$c=\frac{35}{16}, d=\frac{23}{8}$$

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## Linear equations using addition

 Quote by uperkurk So Wolfram is lying to me it seems? Wolfram says the answer is $$c=\frac{35}{16}, d=\frac{23}{8}$$
It seems more likely that you didn't enter the problem correctly into Wolfram Alpha.
 Recognitions: Science Advisor I think you told Wolfram the second equation was $$3c + \frac d 2 = 8$$

 Quote by AlephZero I think you told Wolfram the second equation was $$3c + \frac d 2 = 8$$
Yes, looking back that is what is shows under "Input Result" How would I input the correct format?

Mentor
 Quote by uperkurk Yes, looking back that is what is shows under "Input Result" How would I input the correct format?
If you meant this:
$$\frac{3c + d}{2}$$

you should have written it as (3c + d)/2.

Also, there was some wasted effort when you multiplied the first equation by 2. You didn't need to do that.

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 Quote by uperkurk Yes, looking back that is what is shows under "Input Result" How would I input the correct format?
Use correct brackets.
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