Pair of equations w/ 2 variables

[rasan]

Hello, I am having trouble with one of my homework problems. Usually I would have the teacher explain it in class the next day, but tomorrow is quiz day, and I'd really appreciate any help I could get with it.

The problem concerns solving a pair of equations, each with two variables. Two of the problems on the assignment I understood just fine. They were (5x + 2y = 11 and x+y=4) and (3a + b = 4 and 6a + 2b =8).

Both of those have variables that are fully simplified, thus you don't have to deal with fractions when solving them. The third one, however, does deal with fractions, and it's the one I need help with:

2p + 5q = 15 and 6p + 15q = -29

By process of substitution, I've solved the problem down to the point of:

2p + 5 ((-29 - 6p)/15) = 15

Am I doing it right so far, and how do I proceed? Thanks so much in advance for any help!!

 

[Denis]

The third one, however, does deal with fractions, and it's the one I need help with:
2p + 5q = 15 and 6p + 15q = -29

Multiply 1st equation by 3: 6p + 15q = 45

Are you sure you don't have any typos?

 

[rasan]

The third one, however, does deal with fractions, and it's the one I need help with:
2p + 5q = 15 and 6p + 15q = -29

Multiply 1st equation by 3: 6p + 15q = 45

Are you sure you don't have any typos?

Yeah I'm sure I don't have typos--I double checked.

After multiplying the first by three, it does seem like the equation pair is wrong. It's possible they threw in an unsolvable equation just to give us experience recognizing unsolvable equations, but it would be the first time in this unit that it happened.

Anyway, the longer I look at this, I think that, yes, it's just an unsolvable pair of equations.

Thanks for the help! If you or anyone else wants to confirm what I'm thinking here, it would be great.