Question

line e: y=2/3x+1
line F: y=-3/2x+4

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 e and f
are perpendicular.

Answer 1

Choose these three statements as true:

- The solution to the system is the point of intersection between lines e and f.
- Since the lines are perpendicular, the system has a solution.
- The system is consistent because the lines e and f are perpendicular.

Reason: slopes are 2/3 and −3/2, whose product is −1, so the lines are perpendicular and therefore intersect in exactly one point (a single solution). For reference, the intersection is (x,y) = (18/13, 25/13).