Do the equations y = 23

Question

x + 3 and y = −23
x + 3 form a consistent system?
A.
No, because 23
is not equal to −23
.

B.
No, because 23
is the opposite reciprocal of −23
.

C.
Yes, because 23
is not equal to −23
.

D.
Yes, because 23
is the opposite reciprocal of −23
.

Answer 1

To determine whether the system of equations \( y = 23x + 3 \) and \( y = -23x + 3 \) is consistent, we need to analyze the equations.

1. Identifying the slopes:

   • The first equation \( y = 23x + 3 \) has a slope of \( 23 \).
   • The second equation \( y = -23x + 3 \) has a slope of \( -23 \).

2. Understanding consistency: A system of equations is consistent if there is at least one solution. This happens when the lines intersect at one point or are coincident (the same line). In this case, we have two lines with different slopes (23 and -23), which means they are not parallel and will intersect at exactly one point.

Thus, since the lines have different slopes, the system is consistent.

Therefore, the correct answer is:

C. Yes, because \( 23 \) is not equal to \( -23 \).