Math 1 · Unit 6 · Lesson 4 · part 2 of 5
Three pictures, three answers
Two lines can do three things, and a system of two equations has a matching three answers.
Three pictures, three answers
Two lines can do three things, and a system of two equations has a matching three answers.
One solutionThe lines have different slopes, so they cross exactly once. One point is on both.
No solutionThe lines are parallel: same slope, different y-intercept (Unit 4). They never meet, so no point is on both.
Infinitely many solutionsThe two equations are the same line: same slope, same y-intercept. Every point on it is on both, so every point is a solution.
Predict it without solving. Put both equations in y = mx + b and compare, the elimination habit from Unit 3. Different slopes: one solution. Same slope, different b: none. Same slope, same b: infinitely many. You can call the answer before doing any algebra.