ANSWER
C = -4
EXPLANATION
Given:
15x +20y= -10
6x + 8y= c
Thus we have:
a1 = 15x, b1 = 20y, c1 = -10
and
a2 = 6x, b2 = 8y, c2 = c
The condition now is:
[tex]\frac{a_1}{a_2}\text{ = }\frac{b_1}{b_2}\text{ = }\frac{c_1}{c_2}[/tex]i.e:
[tex]\frac{15x}{6x}=\frac{20y}{8y}\text{ = }\frac{-10}{c}[/tex]Determine c using the x
[tex]\begin{gathered} \frac{15x}{6x}=\frac{-10}{c} \\ \frac{5}{2}\text{ = }\frac{-10}{c} \\ 5c\text{ = -20} \\ c\text{ = -}\frac{20}{5} \\ c\text{ = -4} \end{gathered}[/tex]Determine c using the y
[tex]\begin{gathered} \frac{20y}{8y}\text{ = }\frac{-10}{c} \\ \frac{10}{4}\text{ = }\frac{-10}{c} \\ 10c\text{ = -40} \\ c\text{ = }\frac{-40}{10} \\ c\text{ = -4} \end{gathered}[/tex]Hence, the value of C that will make the systems a dependent system is -4.