For all real values of course, the pair of equations, x-2y=8 and 5x-10

1.	For all real values of course, the pair of equations, x-2y=8 and 5x-10y=c, have a unique solution. Justify whether it is true or false.
Answer» Answer: The STATEMENT given is false. Step-by-step explanation: Given : For all real values of COURSE, the pair of equations, $x-2y=8,5x-10y=c$ have a unique solution. To find : Justify whether it is TRUE or false. Solution : When the system of equation is in FORM $ax+by+c=0, dx+ey+f=0$ then the condition for unique SOLUTIONS is $\frac{a}{d}\neq \frac{b}{e}$ Compare the equations, a=1 , b=-2 , c=-8 , d=5, e=-10, f=-c Substituting the values, $\frac{a}{d}=\frac{1}{5}$ $\frac{b}{e}=\frac{-2}{-10}=\frac{1}{5}$ So, $\frac{a}{d}=\frac{b}{e}$ The given equations are not having unique solutions. Therefore, The statement given is false.