Question

The graph of a system of equations with the same slope will have no solutions

Answer 1

Hey there,

If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of twoparallel lines will have NO solution (no intersection of the lines.)

Hope this helps!

Answer 2

Answer with explanation:

The two linear equations,

1.⇒  y = ax + b

And,2.⇒ y= a x+ c

As well as,3.⇒ 2 y = 2 a x + 2 b or ,⇒ k y= k a x + k b

All the three lines has same slope.

⇒Line 1 and 2 are parallel lines due to different y intercepts, and Line 2 and Line 3 has also same slope but they are coincident.

⇒⇒So,yes when lines are Parallel that is they have same slope has no Solution, but lines which are Coincident having same Slope has infinite number of Solutions.

⇒Incorrect Statement

    The graph of a system of equations with the same slope will have no solutions