Gausselimination with fractions

[Goldberg Variations]

Hello!

I'm trying to solve an equation but I really just fail on the fraction part of it. Guess I need to brush up my highschool math on that part. I have the following equation:

30a + 10b = 38
10a + 4b = 13

Solve a and b.

My first instinct was to subtract row 2 three times on row 1 to get rid of 30a. Which lets me solve b at least and then I can solve a.

I got b = 1/2 (I got it as a negative but I multiplied with *-1 on both sides to get it as a positive, legit?)

Now the real part I am really struggling with is solving a, even though I have b. In the end I got a = 11/10 which seems to me to be very wrong. So could anyone here shed some light on this equation?


Here's my calculation of a:

10a + 4*(1/2) = 13
10a = 13 - 4/2
10a = 13 * 2/2 - 4/2
10a = 26/2 - 4/2
a = 22/20
a = 11/10

And that's it. Looks very wrong to me and sadly I don't have the right answer to this one. Where did I go wrong?

Thanks in advance!

 

[Deleted member 4993]

Hello!

I'm trying to solve an equation but I really just fail on the fraction part of it. Guess I need to brush up my highschool math on that part. I have the following equation:

30a + 10b = 38
10a + 4b = 13

Solve a and b.

My first instinct was to subtract row 2 three times on row 1 to get rid of 30a. Which lets me solve b at least and then I can solve a.

I got b = 1/2 (I got it as a negative but I multiplied with *-1 on both sides to get it as a positive, legit?)

Now the real part I am really struggling with is solving a, even though I have b. In the end I got a = 11/10 which seems to me to be very wrong. So could anyone here shed some light on this equation?


Here's my calculation of a:

10a + 4*(1/2) = 13
10a = 13 - 4/2

10a = 13 - 2 → 10 * a = 11 → a = 11/10

check

30*a + 10* b = 30*(11/10) + 10*(1/2) = 33 + 5 = 38 ........... checks

10*a + 4 * b = 10*(11/10) + 4*(1/2) = 11 + 2 = 13 ........... checks

so the solution is correct.

10a = 13 * 2/2 - 4/2
10a = 26/2 - 4/2
a = 22/20
a = 11/10

And that's it. Looks very wrong to me and sadly I don't have the right answer to this one. Where did I go wrong?

Thanks in advance!

.

 

[Goldberg Variations]

Oh?! That's makes me so happy, guys!

Thanks!