simultaneous equations

Question

Find the value of m for which the simultaneous equations mx − y = 5 and 3x + y = 6 have no solution.

Answer 1

3x + y = 6

and

mx - y = 5

have no solution if they have the same slope, then they are graphically 2 parallel lines that never intersect

solve each equation for y, and make the x coefficients equal

3x+y = 6, y =-3x+6

mx-y = 5, y = mx -5

m=3

3x-y = 5 will have no intersection or solution with 3x+y=6

they're two parallel lines with different y intercepts