Addition elimination method 1 | Systems of equations | 8th grade | Khan Academy

TL;DR

Learn how to solve a system of equations using the elimination method by adding the equations together to eliminate one variable.

Transcript

Use elimination to solve for x and y. And they gave us two equations here-- x plus 2y is equal to 6 and 4x minus 2y is equal to 14. So to solve by elimination, what we do is we're going to add these two equations together so that one of the two variables essentially gets eliminated, gets canceled out. And what we could do right here, we see we have... Read More

Key Insights

• 🪜 The elimination method is used to solve systems of equations by adding them together to eliminate a variable.
• ↔️ Both the left and right sides of an equation must be manipulated equally to maintain equality.
• 🙃 Adding the same expression to both sides of an equation does not change the equality relationship.
• 👻 Solving for one variable allows for substitution and solving for the other variable.

Questions & Answers

Q: What is the first step in solving this system of equations?

The first step is to choose an elimination method and add the equations together to eliminate one variable.

Q: How is the variable 'y' eliminated in this example?

By adding the equations together, the positive 2y and negative 2y terms cancel out, resulting in the elimination of 'y'.

Q: How do you determine the value of 'x'?

After eliminating 'y', the resulting equation is solved for 'x' by simplifying and isolating the 'x' variable.

Q: How do you find the value of 'y'?

Once 'x' is found, it can be substituted back into either of the original equations to solve for 'y' by simplifying and isolating the 'y' variable.

Summary & Key Takeaways

• Two equations are given: x + 2y = 6 and 4x - 2y = 14.

• The elimination method is used by adding the equations together to eliminate the variable 'y'.

• The resulting equation is 5x = 20, solving for x.

• Substituting x = 4 into one of the original equations gives y = 1.

• The solution to the system of equations is x = 4 and y = 1, representing the point of intersection of the lines.