Which of the following pair of linear equations has infinitely many solutions? x+y=1, 2x+2y=2

Q: Which of the following pair of linear equations has infinitely many solutions? x+y=1, 2x+2y=2

The correct answer is B. A pair of linear equations has infinitely many solutions when a₁/a₂ = b₁/b₂ = c₁/c₂. For x+y=1 and 2x+2y=2: 1/2 = 1/2 = 1/2. The second equation is just double the first — they represent the same line. When two equations represent the same line, every point on that line is a solution.

Question

Accepted Answer

A pair of linear equations has infinitely many solutions when a₁/a₂ = b₁/b₂ = c₁/c₂. For x+y=1 and 2x+2y=2: 1/2 = 1/2 = 1/2. The second equation is just double the first — they represent the same line. When two equations represent the same line, every point on that line is a solution.