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y=mx + b --> slope intercept form where slope = m y-intercept = b
To see if a system of linear equations has a solution we should check its slope
y= -1/2x +4 ---------------1
Get second equation in slope intercept form
x+2y = -8
2y =-x -8
y = -1/2x-8/2
y= -1/2x-4 -----------2
In both 1 and 2 the slope is same -1/2
y-intercept is +4 for equation 1 and -4 for equation 2
if the slope is same but the y intercept is different then the two lines are parallel and they have no solution
Please let me know if you need any clarification. I'm always happy to answer your questions.
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