Solutions to three variable system | Algebra II | Khan Academy

TL;DR

The video demonstrates how to solve a system of equations and determines that the system has no solution.

Transcript

Determine whether the system has no solutions or infinite solutions. So they're telling us right from the get go that we're not going to have one nice, clean solution here. So let's just try to solve this system. And so to solve the system we want to eliminate one variable first. So let's say we want to focus on eliminating, let's eliminate the x's... Read More

Key Insights

• ⌛ Systems of equations can be solved by eliminating variables one at a time.
• ❓ Contradictory statements indicate that a system has no solution.
• ✈️ Identical coefficients in two planes imply an infinite number of solutions.

Questions & Answers

Q: What is the goal in solving a system of equations by elimination?

The goal is to eliminate one variable at a time in order to simplify the system and find a solution.

Q: How can you determine if a system of equations has no solution?

If, after eliminating variables and solving the equations, a contradictory statement such as 0 = -21 arises, it means there is no solution.

Q: What would happen if the coefficients of the two planes were the same?

If the coefficients were the same, it would indicate that the two planes are identical and have infinitely many points of intersection.

Q: What are the characteristics of the two planes in this system of equations?

The two planes are parallel and will never intersect, resulting in no solution.

Summary & Key Takeaways

• The video shows the step-by-step process of solving a system of equations by eliminating variables.

• After eliminating variables, the system simplifies to one equation with one unknown.

• However, when incorporating the third constraint, it becomes clear that the system has no solution.