Soru
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.
Çözüm
4.7
(204 Oylar)
Tijen
Usta · 5 yıl öğretmeni
Uzman doğrulaması
Cevap
The correct choices are A and D.
Daha Fazla
## Step 1The 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.## Step 2The 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.## Step 3The 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.## Step 4The 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.## Step 5The 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.## Step 6The 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.