Which value of m will create a system of parallel lines with no solution?
**Two lines are parallel if they have equivalent slopes. If lines are parallel, they may overlap giving us infinitely many solutions.**
~First line is in slope intercept form and has slope 'm'. Continuing on, we have to find the slope of the second line, 'm2'.
8x−4y=12−4y=−8x+12, divide both sides by -4y=2x−3
~From our information, the slope of the second line is 'm2=2'. Meaning, the lines will be parallel if m=2.
~Let's check that by finding y−intercepts.
~Intercept of first line is y1=−6 and intercept of second line is y2=−3, so lines do not overlap. Thus, for m=2 we have parallel lines with no solutions.