Question

question 3
1 pts
consider the system of equations:
unknown node type: span
which statement best describes the solution to this system?
the system has infinitely many solutions because the equations are equivalent.
the system has no solution because the lines have the same slope but different y - intercepts.
the system has one solution because the slopes are different
the system has one solution because the lines intersect at exactly one point.
question 4
1 pts
the graph of a system of equations shows two lines that overlap completely.
what does this tell you about the system?
the system has exactly two solutions.
the system has infinitely many solutions because every point on the line satisfies both equations.
the system has one solution at the point where the lines cross.
the system has no solution because the lines never intersect.

Explanation:

Question 3

To determine the solution of a system of linear equations, we analyze the slopes and y - intercepts of the lines. If two lines have the same slope but different y - intercepts, they are parallel and never intersect, so the system has no solution. If the equations are equivalent, the lines are the same and there are infinitely many solutions. If slopes are different, the lines intersect at one point (one solution). Since the option about same slope and different y - intercepts (no solution) is a valid case for a system with parallel lines.

When two lines in a system of equations overlap completely, they are the same line. Every point on this line will satisfy both equations (since the equations represent the same line), so there are infinitely many solutions. A system of linear equations can have 0, 1, or infinitely many solutions. Two overlapping lines can't have exactly two solutions, one solution (as they are the same line, not intersecting at a single point) or no solution (as they overlap, so they do intersect at all points on the line).

Answer:

The system has no solution because the lines have the same slope but different y - intercepts.

Question 4