Solving system with elimination | Algebra | Khan Academy

TL;DR

Learn how to find the intersection point of two linear equations by graphing them and identifying the X and Y coordinates.

Transcript

• [Instructor] So we have a system of two linear equations here. This first equation, X minus four Y is equal to negative 18, and the second equation, negative X plus three Y is equal to 11. Now what we're gonna do is find an X and Y pair that satisfies both of these equations. That's what solving the system actually means. As you might already hav... Read More

Key Insights

• 😥 Solving a system of linear equations involves finding the point where the equations intersect on a graph.
• 👈 Adding the left side terms of both equations cancels out the X values, leaving us with an equation only containing Y.
• 😑 To maintain equality, we add a value equivalent to the eliminated variable expression, which is derived from the second equation.
• ☺️ The Y value is then substituted back into one of the equations to solve for the X value.
• 😥 The X and Y coordinates of the intersection point represent the solution to the system of equations.
• 🫥 Graphing the equations allows visualizing the lines and their intersection point.
• 🫥 The lines represent all the X and Y pairs that satisfy each equation individually.

Questions & Answers

Q: What is the purpose of solving a system of linear equations?

Solving a system of linear equations helps us find the point where both equations intersect. This point represents the X and Y values that satisfy both equations simultaneously.

Q: How can we eliminate one of the variables in the equations?

By adding the left side terms of both equations, we can eliminate the X values. This leaves us with one equation containing only the Y value, which we can then solve for.

Q: Can we add any value to the right side of the equation?

No, we need to add a value that is equivalent to the eliminated variable expression. In this case, we use the number 11, derived from the second equation, to maintain equality.

Q: How do we find the X value?

Once we have the Y value, we can substitute it into either equation and solve for X. Regardless of which equation we choose, we will obtain the same X value.

Summary & Key Takeaways

• This video explains the process of finding the intersection point of two linear equations by graphing them.

• By adding the left side terms of both equations, the X values cancel out, allowing us to solve for the Y value.

• The Y value is then substituted back into one of the equations to solve for the X value.