Question

when using substitution to solve systems of equations that have no solution or infinitely many solutions, the variable terms are the same on both sides. how is the solution determined by the constants in the equations?

if the constants are the same, the equations represent lines that must be ▼ so the system of equations has ▼ if the constants are different, the equations represent lines that are ▼ so the system of equations has ▼

Explanation:

1. For the first blank (relationship of lines when constants are same): When variable terms are same and constants are same, the equations are equivalent, so lines are "coinciding" (same line, infinitely many solutions).
2. Second blank (solution when constants same): Since lines coincide, system has "infinitely many solutions".
3. Third blank (relationship of lines when constants different): With same variable terms but different constants, lines are "parallel" (same slope, different y - intercepts, never meet).
4. Fourth blank (solution when constants different): Parallel lines have "no solution".

Answer:

First blank: coinciding; Second blank: infinitely many solutions; Third blank: parallel; Fourth blank: no solution