Question

Question content area top
Part 1
Think About the Process  What must be true for a system of equations to have exactly one solution​? How many solutions does this system​ have?
y equals five fourths x minus 8
y equals 1.25 x minus 8
Question content area bottom
Part 1
What must be true for a system of equations to have exactly one solution​?
A.
The slopes must be equal and the y dash intercepts must not be equal.
B.
The slopes must not be equal.
C.
The slopes must be equal and the y dash intercepts must be equal.

Answer 1

Correct choice: B. The slopes must not be equal.

Reason: The two equations are y = (5/4)x − 8 and y = 1.25x − 8. Since 1.25 = 5/4 and both y‑intercepts are −8, the lines are identical, so the system has infinitely many solutions.