Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]
Transform this matrix in a row-echelon form:
[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex] [tex]R_{2} = 3R_{2}+R_{1}[/tex] [tex]\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right][/tex]
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
