Question

Look at the system of equations below. Which of these statements must be true? Check ALL that applies.

y= -2x+5
y= -2x+3

The statements are:
1.) The lines intersect at one point
2.) The equations represent parallel lines
3.) The equations represent the same line
4.) The solution to the system will have no solution
5.) The solution to the system will have infinitely many solutions
6.) The system is inconsistent
7.) The system is consistent
8.) The system is independent
9.) The system is dependent

Answer 1

The statements that must be true are:

3.) The equations represent the same line
5.) The solution to the system will have infinitely many solutions
7.) The system is consistent
9.) The system is dependent

Step-by-step explanation:

Both equations have the same slope of -2, which means they are parallel. However, they also have different y-intercepts, which means they are not the same line. Since they are not the same line and have the same slope, they must be parallel lines.

Since the equations represent parallel lines, they will never intersect and there will be no solution to the system. However, since the two equations are equivalent, they have the same solution set, which means the system has infinitely many solutions.

Since the system has infinitely many solutions and the equations are not independent, the system is consistent and dependent.