The elimination method is a great way to solve systems of linear equations. It's especially useful when you have several variables to deal with. Let’s break it down step by step:
Pick a Variable to Get Rid Of: First, you need to choose which variable you want to eliminate. This means looking for equations that can easily combine to cancel out that variable.
Multiply the Equations: Sometimes, you may need to multiply one or both equations by a number. This helps match the numbers in front of the chosen variable so they can cancel each other out. For example, if you have the equations (2x + 3y = 6) and (4x - y = 8), you could multiply the second equation by 3. This gives you (12x - 3y = 24).
Combine the Equations: Next, you add or subtract the equations together. This step is where one variable disappears. For example, if you add the two new equations: (2x + 3y + 12x - 3y = 6 + 24), the (y) terms will cancel out, leaving you with a simpler equation.
Solve the New Equation: Now you’re left with an easier equation to solve. Once you find the value of one variable, you can put it back into one of the original equations to find the value of the other variable.
In summary, the elimination method is super useful for solving equations quickly, especially when you have a lot of them!
The elimination method is a great way to solve systems of linear equations. It's especially useful when you have several variables to deal with. Let’s break it down step by step:
Pick a Variable to Get Rid Of: First, you need to choose which variable you want to eliminate. This means looking for equations that can easily combine to cancel out that variable.
Multiply the Equations: Sometimes, you may need to multiply one or both equations by a number. This helps match the numbers in front of the chosen variable so they can cancel each other out. For example, if you have the equations (2x + 3y = 6) and (4x - y = 8), you could multiply the second equation by 3. This gives you (12x - 3y = 24).
Combine the Equations: Next, you add or subtract the equations together. This step is where one variable disappears. For example, if you add the two new equations: (2x + 3y + 12x - 3y = 6 + 24), the (y) terms will cancel out, leaving you with a simpler equation.
Solve the New Equation: Now you’re left with an easier equation to solve. Once you find the value of one variable, you can put it back into one of the original equations to find the value of the other variable.
In summary, the elimination method is super useful for solving equations quickly, especially when you have a lot of them!