Solving systems of equations by elimination | Algebra Basics | Khan Academy

TL;DR

Learn how to solve systems of equations and word problems using elimination method in this detailed explanation.

Transcript

Let's explore a few more methods for solving systems of equations. Let's say I have the equation, 3x plus 4y is equal to 2.5. And I have another equation, 5x minus 4y is equal to 25.5. And we want to find an x and y value that satisfies both of these equations. If you think of it graphically, this would be the intersection of the lines that represe... Read More

Key Insights

• 🫥 Solving systems of equations involves finding the intersection point of two lines.
• 🪜 Adding or subtracting equations can eliminate one variable and simplify the system.
• 🔑 The elimination method is a useful tool for solving word problems.
• ❓ Verifying the solution by substituting the values back into the equations ensures its accuracy.
• 😫 Assigning variables and setting up equations is essential in solving word problems.
• 🍉 Different coefficients can be used to make terms cancel out when using the elimination method.
• 👻 Manipulating equations by adding or subtracting allows for simplification and solution finding.

Questions & Answers

Q: How can we eliminate one variable in a system of equations?

We can add or subtract the equations to eliminate one variable. By carefully selecting a coefficient, we can make the terms cancel out.

Q: Why can we add different values to both sides of an equation?

As long as we add the same value to both sides, the equation remains balanced. This allows us to manipulate the equation and simplify it.

Q: Can we solve word problems using the elimination method?

Yes, the elimination method can be used to solve word problems involving multiple equations. By assigning variables and setting up equations, we can find the values of the unknowns.

Q: How do we verify if the solution is correct?

To verify the solution, substitute the values of x and y into both equations. If the equations hold true, the solution is correct.

Summary & Key Takeaways

• Graphically, solving a system of equations means finding the intersection point of the two lines representing the equations.

• By adding or subtracting the two equations, we can eliminate one variable and solve for the other variable.

• Using the elimination method, we can find the values of x and y that satisfy both equations.