Steve wants to create a system of equations so that the system has no solution. Which of these can Steve do? Check all that apply. Create a pair of equations with the same slope and different y-intercepts. Create a pair of lines in which one line lies directly on top of the other. Create a pair of equivalent equations. Create a pair of lines that will always stay the same distance apart. Create a pair of lines that intersect at only one point.

## Step 1<br />The problem is asking us to identify the conditions under which a system of equations has no solution. In the context of linear equations, a system has no solution when the lines represented by the equations are parallel. This means that the lines have the same slope but different y-intercepts.<br /><br />## Step 2<br />The first option, "Create a pair of equations with the same slope and different y-intercepts", is a correct choice. This is because such equations represent parallel lines, which never intersect and thus have no solution.<br /><br />## Step 3<br />The second option, "Create a pair of lines in which one line lies directly on top of the other", is not a correct choice. This is because such lines are identical and have infinitely many solutions, as every point on the line is a solution to the system.<br /><br />## Step 4<br />The third option, "Create a pair of equivalent equations", is also not a correct choice. Equivalent equations represent the same line, and thus they have infinitely many solutions.<br /><br />## Step 5<br />The fourth option, "Create a pair of lines that will always stay the same distance apart", is a correct choice. This is because such lines are parallel and never intersect, which means they have no solution.<br /><br />## Step 6<br />The fifth option, "Create a pair of lines that intersect at only one point", is not a correct choice. This is because such lines intersect at exactly one point, which means they have one solution.