Question

x - y = 1
show your work
check it!
options: 1, infinitely many solutions, no solution

Explanation:

Step1: Analyze the equation type

The equation given is \(x - y = 1\), which is a linear equation in two variables (x and y). A linear equation in the form \(ax+by = c\) (here \(a = 1\), \(b=- 1\), \(c = 1\)) has infinitely many solutions because for any value of \(x\), we can find a corresponding \(y\) (e.g., if \(x = 2\), then \(y=x - 1=1\); if \(x = 3\), then \(y = 2\), and so on) or we can rewrite it as \(y=x - 1\), which represents a straight line, and a straight line has infinitely many points (solutions) on it.

Step2: Compare with solution types

• "No Solution" would be for equations like \(0x + 0y=c\) where \(c

eq0\), which is not our case.

• "1" is not a valid description for the number of solutions of a linear equation in two variables (unless it's a system with specific conditions, but here it's a single equation).
• "Infinitely Many Solutions" matches our analysis of the linear equation \(x - y = 1\) as it represents a line with infinite points.

Answer:

Infinitely Many Solutions