Classify a system of equations by graphing

Learning Objectives Graph two linear equations on the same coordinate plane. Identify the point of intersection of two lines, if it exists. Determine if two lines are parallel or coincident from their graphs. Classify a system of linear equations as having one solution, no solution, or infinitely many solutions based on its graph. Relate the graphical classification to the terms 'consistent', 'inconsistent', and 'dependent'. Explain what a 'solution' means for a system of two linear equations. Ever tried to find the exact spot where two paths cross? 🗺️ In math, we can do something similar with lines to solve problems! In this lesson, you'll learn how to draw two straight lines on a graph and use their relationship to understand i...

TermDefinitionExample System of Linear EquationsTwo or more linear equations that are considered together. We are looking for values that satisfy all equations at once.The system includes the equations: $y = 2x + 1$ and $y = -x + 4$. Solution to a SystemThe point (x, y) that makes *all* equations in the system true. Graphically, it's the point where the lines intersect.For the system $y = 2x + 1$ and $y = -x + 4$, the solution is (1, 3) because 3 = 2(1)+1 and 3 = -(1)+4. Consistent SystemA system of equations that has at least one solution (meaning the lines intersect at one point or are the same line).A system where the lines cross at (2, 5) is consistent. Inconsistent SystemA system of equations that has no solution (meaning the lines are parallel and never intersect).A system wher...

One Solution (Consistent & Independent) If two lines intersect at exactly one point, the system has one unique solution. To classify, graph both equations. If they cross at a single point, that point is the solution, and the system is consistent and independent. No Solution (Inconsistent) If two lines are parallel and never intersect, the system has no solution. Graph both equations. If they have the same slope but different y-intercepts, they are parallel and will never meet. The system is inconsistent. Infinitely Many Solutions (Consistent & Dependent) If two equations represent the exact same line, the system has infinitely many solutions. Graph both equations. If one line lies directly on top of the other, every point on the line is a solution. The system...