Linear equations using addition

In summary, When using Wolfram Alpha, make sure to use correct brackets and format for the equations to get accurate answers. In this case, the correct format for the second equation would be (3c + d)/2, and there was no need to multiply the first equation by 2.
  • #1
uperkurk
167
0
I'm probably making a silly mistake or Wolfram Alpha is lying to me.

Question: Find the value of c and d.

[itex]3d=13-2c[/itex]

[itex]\frac{3c+d}{2}=8[/itex]

Rearranged, simplified and multiply each equation by 2:

[tex]6d+4c=26[/tex]
[tex]d+3c=16[/tex]

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

[tex]18d+12c=78[/tex]
[tex]-4d-12c=-64[/tex]

Then add them and find what d is worth:

[tex]14d=14[/tex]

[tex]d=1[/tex]

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

[tex]3(1)+2c=13[/tex]
[tex]3+2(c)=13[/tex]
[tex]c=5[/tex]

[tex]d=1, c=5[/tex]

What am I doing wrong? Sorry if this is the long winded way to do it.
 
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  • #2
Your answer is correct, as you can verify by plugging ##d = 1## and ##c = 5## into the two given equations.
 
  • #3
jbunniii said:
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 [tex]c=\frac{35}{16}, d=\frac{23}{8}[/tex]
 
  • #4
uperkurk said:
So Wolfram is lying to me it seems?

Wolfram says the answer is [tex]c=\frac{35}{16}, d=\frac{23}{8}[/tex]
It seems more likely that you didn't enter the problem correctly into Wolfram Alpha.
 
  • #5
I think you told Wolfram the second equation was
$$3c + \frac d 2 = 8$$
 
  • #6
AlephZero said:
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?
 
  • #7
uperkurk said:
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.
 
  • #8
uperkurk said:
Yes, looking back that is what is shows under "Input Result" How would I input the correct format?

Use correct brackets.
 

1. What is a linear equation using addition?

A linear equation using addition is an equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. It is called a linear equation because when graphed, it forms a straight line.

2. How do you solve a linear equation using addition?

To solve a linear equation using addition, you need to isolate the variable on one side of the equation. This can be done by using inverse operations, such as subtracting or adding the same number to both sides of the equation. Once the variable is isolated, the solution can be found by substituting the value of the variable back into the equation.

3. What is the importance of slope in a linear equation using addition?

The slope in a linear equation using addition represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It tells us how much y changes for every one unit change in x. The slope can also indicate the direction of the line, whether it is increasing or decreasing.

4. Can a linear equation using addition have more than one solution?

No, a linear equation using addition can only have one solution. This is because there is only one value of the variable that will make the equation true. If there are multiple variables in the equation, it will have infinitely many solutions.

5. How are linear equations using addition used in real life?

Linear equations using addition are used in various fields of science and mathematics, such as physics, economics, and engineering. They can be used to model real-life situations, such as calculating the growth of a population or predicting the future value of an investment. They are also used in designing experiments and analyzing data.

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