Grade 10 Solving Linear Systems - How many solutions?

Without solving a linear system you should be able to identify how many solutions there will be. We do this by looking at the lines in slope y-intercept form to see if the lines are parallel and then checking the y-intercept. If slope and y-intercept are the same, there will be an infinite number of solutions as they are the same line. You can also check to see if the lines are just a multiple of each other. Same slope, different y-intercept will mean that there is NO point of intersection as the lines are parallel. Different slopes will give you one point of intersection. Easy!!