Question

Which statements about the system are true? (Choose three.)

Responses
The solution to the system is the point of intersection between lines
.
The solution to the system is the point of intersection between lines e A n d f .
It is impossible for
to equal both

and

simultaneously; therefore, the system has no solution.
It is impossible for y to equal both 2 thirds x plus 1 and negative 3 halves x plus 4 simultaneously; therefore, the system has no solution.
The system is inconsistent because the lines are perpendicular.
The system is inconsistent because the lines are perpendicular.
The system is consistent because the lines are parallel.
The system is consistent because the lines are parallel.
Since the lines are perpendicular, the system has a solution.
Since the lines are perpendicular, the system has a solution.
The system is consistent because the lines
are perpendicular.

Answer 1

True choices (three):

1. The solution to the system is the point of intersection between the lines.
2. Since the lines are perpendicular, the system has a solution.
3. The system is consistent because the lines are perpendicular.

Reason: the two equations are y = (2/3)x + 1 and y = (−3/2)x + 4. Their slopes 2/3 and −3/2 are negative reciprocals, so the lines are perpendicular and therefore intersect in exactly one point (so the system is consistent). Solving gives the intersection (x,y) = (18/13, 25/13).