Question

2x-y=4 and 2x-y=3

Answer 1

We can solve this system by substitution:

if 2x - y = 4, we can manipulate this to arrive at:

=> 2x - 4 = y

Substitute in 2x - 4 to the second equation wherever we see a y:

If: 2x - y = 3

=> 2x -(2x - 4) = 3
=> 2x - 2x + 4 = 3
=> 4 = 3 ... This is obviously not true.

Thus, this system has no solution.

If you look at the lines in a different form:

y = 2x - 4
y = 2x - 3

You can see that we have two lines with the same slope: 2. They both begin at different y-intercepts: -4 and -3. Thus, they are parallel lines, and parallel lines do not intersect (meaning there is no solution to the system) unless they have the same y-intercept.

Hope that helps =)