In the elimination method, you multiply one or both equations by a suitable constant (not necessarily 2) so that when you add or subtract the equations, one of the variables cancels out. The goal is to create a situation where one of the variables has the same coefficient but opposite signs in both equations, making it easier to eliminate it.
The choice of the constant you multiply by depends on the specific problem. It doesn't always have to be 2; it could be any number that helps you eliminate one of the variables. Here are the general steps:
1. Examine the coefficients of one of the variables (let's say variable x) in both equations. If they are already opposites (e.g., 3x and -3x), you don't need to multiply by a constant. If not, proceed to the next step.
2. Choose a constant (often referred to as a "multiplying factor") that, when you multiply one or both equations by it, will make the coefficients of one of the variables opposites. For example, if you have 2x and 3x in your equations, you might multiply the first equation by 3 and the second equation by 2 to make the coefficients of x opposites (6x and 6x).
3. Add or subtract the equations to eliminate one variable, and then solve for the remaining variable.
The specific constant you use depends on the equations you are working with. The key is to manipulate the equations so that when you add or subtract them, one variable cancels out. You can use any number that accomplishes this, not just 2.
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Step-by-step explanation:
In the elimination method, you multiply one or both equations by a suitable constant (not necessarily 2) so that when you add or subtract the equations, one of the variables cancels out. The goal is to create a situation where one of the variables has the same coefficient but opposite signs in both equations, making it easier to eliminate it.
The choice of the constant you multiply by depends on the specific problem. It doesn't always have to be 2; it could be any number that helps you eliminate one of the variables. Here are the general steps:
1. Examine the coefficients of one of the variables (let's say variable x) in both equations. If they are already opposites (e.g., 3x and -3x), you don't need to multiply by a constant. If not, proceed to the next step.
2. Choose a constant (often referred to as a "multiplying factor") that, when you multiply one or both equations by it, will make the coefficients of one of the variables opposites. For example, if you have 2x and 3x in your equations, you might multiply the first equation by 3 and the second equation by 2 to make the coefficients of x opposites (6x and 6x).
3. Add or subtract the equations to eliminate one variable, and then solve for the remaining variable.
The specific constant you use depends on the equations you are working with. The key is to manipulate the equations so that when you add or subtract them, one variable cancels out. You can use any number that accomplishes this, not just 2.