Respuesta :
Answer: The given system of equations will have infinite number of solution.
Step-by-step explanation: We are given to solve the following system of equations by substitution method :
[tex]x-3y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-6y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]x-3y=4\\\\\Rightarrow x=4+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]2(4+3y)-6y=8\\\\\Rightarrow 8+6y-6y=8\\\\\Rightarrow 8=8,[/tex]
which is always true.
So, the given system of equations will have infinite number of solutions.
Let y = k, a real number. Then, from equation (iii), we get
[tex]x=4+3k.[/tex]
Thus, all the solutions of the given system are given by
(x, y) = (4+3k, k).
