Question

A system of equations is shown below.

{
6.3
x
−
4.7
y
=
−
9
−
6.3
x
+
4.7
y
=
8

Which of the following best explains why there is no solution to the system?

A.
Adding the two equations results in 0 = –1, which is a false statement.

B.
The two equations describe lines with the same slope, which means they are the same line.

C.
Subtracting the two equations results in 0 = 0, which is a true statement.

D.
The two equations have a single point of intersection at the point (0,–1)

Answer 1

A.

Add the two equations: (6.3x − 4.7y) + (−6.3x + 4.7y) = −9 + 8 gives 0 = −1, a contradiction. The system is inconsistent (equivalent to two parallel lines with the same slope but different intercepts), so there is no solution.