Question

Rewrite the equation 3x+y=7 in slope-intercept form to select the statement that correctly describes the system of equations {3x+y=7 ; y=-3x+7

Statement #1: The system of equations has no solutions because the graphs of the two equations are parallel lines.

Statement #2: The system of equations has an infinite number of solutions because the graphs of the two equations occupy the same line.

Answer 1

Rewrite 3x + y = 7 as y = -3x + 7 (subtract 3x from both sides).

Since the second equation is y = -3x + 7 as well, the two equations are the same line, so the system has infinitely many solutions.

Therefore Statement #2 is correct.