Question

2 start with the linear equation ( y = -2x + 0.5 ). write an equation that results in a system of equations with the given number of solutions.
a. no solution
b. one solution
c. infinitely many solutions

Explanation:

Step1: No solution (parallel lines)

For a system with no solution, create a line with the same slope ($-2$) but different y-intercept. Example: $y = -2x + 1$

Step2: One solution (intersecting lines)

For a system with one solution, create a line with a different slope. Example: $y = 3x + 0.5$

Step3: Infinitely many solutions

For infinitely many solutions, create an equivalent line (same slope and intercept, rewritten). Example: $2y = -4x + 1$ (multiply original by 2)

Answer:

a. $y = -2x + 1$ (any line with slope $-2$, y-intercept $
eq 0.5$)
b. $y = 3x + 0.5$ (any line with slope $
eq -2$)
c. $2y = -4x + 1$ (any equivalent rewrite of $y = -2x + 0.5$)