Given the system of equations :
8x + 16y = 15 →(1)
x = 5 - 2y →(2)
By substitution with x from equation (2) at the equation (1) :
[tex]8(5-2y)+16y=15[/tex]Solve for y :
[tex]\begin{gathered} 8\cdot5-8\cdot2y+16y=15 \\ 40-16y+16y=15 \\ 40=15 \end{gathered}[/tex]The last result is un logic , which mean the given system of equation represents two lines with the same slope and different y- intercepts
So, the given system represents a parallel lines
So, the answer is option C. the solution set is the empty set
