Question

what does it mean if a system of equations graphs as two intersecting lines?
a. the system cannot be solved.
b. the system has no solution.
c. the system has infinitely many solutions.
d. the system has one solution.

which of the following represents a line with no y-intercept?
a. $y=5x$
b. $x=5$
c. $y=0x+0$
d. $y=-x$

Explanation:

Step1: Analyze intersecting lines

A system of two linear equations graphs as two intersecting lines when the lines cross at exactly one point. This single point is the unique solution to the system, so the correct option is d.

Step2: Identify no y-intercept line

A line has no y-intercept if it never crosses the y-axis (where $x=0$). For $x=5$, this is a vertical line parallel to the y-axis, so it never intersects the y-axis.

• For $y=5x$, the y-intercept is $(0,0)$.
• For $y=0x+0$, the y-intercept is $(0,0)$.
• For $y=-x$, the y-intercept is $(0,0)$.

Thus, the correct option is b.

Answer:

1. d. The system has one solution.
2. b. $x=5$