Solve the system.
#color(white)a6x-3y=-13#
#14x-7y=color(white)a-8#
Multiply the first equation by 7 and the second by -3.
#color(white)a7(color(white)a6x-3y=-13)#
#-3(14x-7y=color(white)a-8#
#color(white)(a^1)42x-21y=-91#
#-42x+21y=color(white)(aa^1)24#
Add the two equations.
#0x+0y=-67#
#0=-67color(white)(aaa)#FALSE!
There is no solution to this system of equations. In other words, the two lines represented by these equations never intersect and they must be parallel.
Another way to show this is to rearrange the equations in slope-intercept form #y=mx+b# where #m=slope.
#color(white)a6x-3y=-13#
#-6xcolor(white)(aaaaa)-6x#
#-3y=-6x-13#
#(-3y)/-3=(-6x)/-3-13/-3#
#y=color(red)2x+13/3color(white)(aaa)#The slope of the 1st line is 2
#14x-7y=color(white)a-8#
#-14xcolor(white)(aaaa)-14x#
#-7y=-14x-8#
#(-7y)/-7=(-14x)/-7-8/-7#
#y=color(red)2x+8/7color(white)(aaa)# The slope of the 2nd line is 2.
Both have the same slope of #m=2#, so the lines must be parallel.
