The given system of equations is graphed on the coordinate plane.
line e: y=23x+1
line f: y=−32x+4
Which statements about the system are true? (Choose three.)
Responses
The solution to the system is the point of intersection between lines e and f
.
The solution to the system is the point of intersection between lines e and f
.
It is impossible for y
to equal both 23x+1
and −32x+4
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.
The correct statements are:
1. The solution to the system is the point of intersection between lines e and f.
2. It is impossible for y to equal both 23x+1 and −32x+4 simultaneously; therefore, the system has no solution.
3. The system is consistent because the lines e and f are perpendicular.