Question

Think About the Process  What must be true for a system of equations to have no solution​? How many solutions does this system​ have?
y equals seven fourths x minus 2
y equals one third x minus 2
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Part 1
What must be true for a system of equations to have no 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 answer: C. The slopes must be equal and the y-intercepts must not be equal (parallel lines) for no solution.

For the given system y = (7/4)x − 2 and y = (1/3)x − 2 the slopes are different, so there is exactly one solution. Solving (7/4)x − 2 = (1/3)x − 2 gives (7/4)x = (1/3)x, so x = 0 and y = −2. The solution is (0, −2).