Solving for h in a Consistent Linear System

[beanryu]

hello.
please help!

this is the problem:
determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

1 -3 -2
5 h -7

i tried replacing and scaling... but it seems there are always 2 variable in this.
can you guys help me solve this problem?

 

[J77]

Is that an augmented system:

1x-3y=-2
5x+hy=-7

?

 

[beanryu]

is that not?

 

[beanryu]

is the answer any number... because with everynumber, there is a different solution to x and y?... probably true?

 

[beanryu]

ohkay... i think i got the answer... h cannot be 15, because than it will be

1 -3 -2
0 0 3
this show that it will be inconsistent...

 

[HallsofIvy]

No, you've "lost a sign". The row reduction of
$$\left[\begin{array}{ccc}1 & -3 & -2 \\ 5 & h & 7\end{array}\right]$$
is
$$\left[\begin{array}{ccc}1 & -3 & 2\\ 0 &h+ 15 & 3\end{array}\right]$$

What must h be so that is inconsistent?