Q:

Determine whether each pair of equations has no solutions, one solution, orinfinitely many solutionsy=2 x and y=-2xy=-x - 2 and y = -x - 6y = 9x - 1 and y = x + 9y = 3x + 4 and 2y = 6x + 8y=-3 and x = -6​

Accepted Solution

A:
Answer:y=2 x and y=-2x  ONE y=-x - 2 and y = -x - 6  NONE y = 9x - 1 and y = x + 9  ONE y = 3x + 4 and 2y = 6x + 8  INFINITE y=-3 and x = -6​ ONEExplanation:Any two equations (with y value isolated, meaning y has no coefficient) that have the same slope will have no solutions because they are parallel. Parallel lines never meet. For example:y=-x - 2 and y = -x - 6 They both have a slope of -1. The slope is the number attached to the "x".If two equations are equivalent, they will have infinite solutions. Equivalent equations can be found when a whole equation is multiplied or divided by a number. For example:y = 3x + 4 and 2y = 6x + 8 When you double every term in the first equation, it becomes:2y = (2)3x + (2)4It's the same as 2y = 6x + 8 .Any other case will have one solution.