Solving system of equations by graphing (consistent vs. inconsistent)

TL;DR

Learn how to solve a system of equations with two variables by graphing the equations on the same coordinate plane.

Transcript

in this video I will show you how to solve a 2 by 2 system of equations by graphing and I also show you guys the three possible situations that we encounter with and let's look at the first one to solve a system equations by graphing we are going to first graph the first equation and then grab the second equation procured on the same XY plane and w... Read More

Key Insights

• 😃 Solving a 2x2 system of equations by graphing involves isolating variables and converting equations to y = mx + b form.
• 📈 The three possible outcomes when graphing a system are: one solution, no solution, or infinitely many solutions.
• 🍉 Understanding the terms consistent, inconsistent, independent, and dependent helps classify the system.
• 🏮 Graph paper is recommended for accurate graphing.

Questions & Answers

Q: How do you graph a system of equations on the same coordinate plane?

To graph a system of equations, first isolate one variable in each equation and rewrite it in the form y = mx + b. Then, plot the y-intercept of each equation and use the slope to locate another point. Connect the points to form the graph.

Q: What are the three possible situations when graphing a system of equations?

The three possible situations are:

1. The lines intersect at one point, indicating one solution to the system of equations.
2. The lines are parallel and never intersect, indicating no solution.
3. The lines overlap and are the same, indicating infinitely many solutions.

Q: How do you determine if a system of equations is consistent or inconsistent?

If a system of equations has at least one solution, it is consistent. If it has no solutions, it is inconsistent.

Q: What does it mean for a system of equations to be independent or dependent?

If a system of equations consists of different lines, it is independent. If the lines are the same, it is dependent.

Summary & Key Takeaways

• To solve a system of equations by graphing, first isolate one variable in each equation to graph them in the form y = mx + b.

• Plot the y-intercept and use the slope to locate another point on the graph.

• The three possible situations are: the lines intersect at one point (one solution), the lines are parallel (no solution), and the lines overlap (infinitely many solutions).