Deedra has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7. What must be true about the two lines?

Accepted Solution

we can take a peek at two of those lines  hmmm say y = 5x + 3 and y = 5x + 7.let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.since y = y then5x + 3 = 5x + 73  = 7    what the?well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.