Question

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 2
y equals 1.25 x minus 2
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Part 1
What must be true for a system of equations to have exactly one solution​?
A.
The slopes must not be equal.
B.
The slopes must be equal and the y dash intercepts must be equal.
C.
The slopes must be equal and the y dash intercepts must not be equal.

Answer 1

Part 1: A. The slopes must not be equal (then the lines intersect in exactly one point).

This system: y = (5/4)x − 2 and y = 1.25x − 2 have the same slope (5/4 = 1.25) and the same y‑intercept (−2), so they are the same line. Therefore there are infinitely many solutions.