To create a system of equations in slope-intercept form with no solution, we need two lines that are parallel, as parallel lines never intersect.

In slope-intercept form ($y = mx + b$), two lines are parallel if they have the same slope ($m$) but different $y$-intercepts ($b$).

Here’s an example of such a system:

1. First equation: $y = 2x + 1$
2. Second equation: $y = 2x + 3$

These equations both have a slope of 2, which makes the lines parallel, but different $y$-intercepts (1 and 3), ensuring they will never intersect and therefore have no solution.

So, for the blanks:

• Blank 1: $y = 2x + 1$
• Blank 2: $y = 2x + 3$

Would you like further details or explanations?

Here are some related questions to deepen your understanding:

1. What condition ensures that two lines in slope-intercept form have no solution?
2. How can you tell if two lines are parallel just by looking at their equations?
3. What happens if the two lines have the same slope and same intercept?
4. How would the system look if it had infinitely many solutions instead?
5. Why do different $y$-intercepts prevent two lines from intersecting?

Tip: In slope-intercept form, always focus on the slope ($m$) to determine if lines are parallel, perpendicular, or intersecting.