Answer:
(a) Proof explained below
(b) The two lines are parallel
Step-by-step explanation:
(a) In the second equation express [tex]x[/tex] in terms of [tex]y[/tex] to get:
[tex]x=2y-8[/tex]
Then, substitute [tex]x[/tex] for [tex]2y-8[/tex] in the first equation to get:
[tex]3(2y-8)-6y=-12[/tex]
Open parentheses using the distributive property ([tex]a(b-c)=ab-ac[/tex]) which results in:
[tex]6y-24-6y=-12[/tex]
Combine like terms to reach:
[tex]-24=-12[/tex], which is not true. Therefore, for any values of [tex]x[/tex] and [tex]y[/tex], the systems of equations will have no solutions.
Since the two lines have no solutions, that means that they are parallel.
Hope this helps :)
