Question

5
the graphs of the given equations are shown.
$y = -3$
$y = \frac{7}{2}$
graph of two horizontal lines, y = -3 (blue) and y = 7/2 (red), on a coordinate plane
how many solutions are shown by the linear graphs?
a. exactly one real solution at $x = 7$
b. exactly one real solution at $x = -13$
c. no real solutions
d. infinite real solutions

Explanation:

The two linear graphs \( y = -3 \) and \( y=\frac{7}{2} \) are horizontal lines (parallel, as they have the same slope, \( m = 0 \)) and distinct (different \( y \)-intercepts). Parallel lines with different \( y \)-intercepts never intersect, so there are no real solutions to the system of these linear equations.

Answer:

C. no real solutions