1. 4x + 8y = 12....divide by 4 x + 2y = 3 2y = -x + 3 y = -1/2x + 3/2...slope is -1/2, y int is 3/2
x + 2y = -3 2y = -x - 3 y = -1/2x - 3/2...slope is -1/2 and y int is -3/2
when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent ================= 2. y = 2x - 1...slope is 2 and y int is -1 y = -2x + 5 ...slope is -2 and y int is 5 when the slopes are different and the y int are different, then there is 1 solution making it independent ================= 3. 4x - 12y = 8...divide by 4 x - 3y = 2 same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent
