In the elimination method, what is a common technique to eliminate a variable?

In the elimination method, what is a common technique to eliminate a variable?

• A. Line up terms in both equations and add to cancel a variable
• B. Graph the two equations and pick the intersection
• C. Solve one equation for a variable and substitute into the other
• D. Solve the system by finding a point on a plotted line

Answer: (A)

Eliminating a variable by adding the equations until one variable disappears is the idea here. You rewrite the system in standard form and align like terms so that the coefficients of one variable sum to zero. Then you add (or subtract) the equations to cancel that variable, leaving you with an equation in a single variable. After solving for that variable, you substitute back into one of the original equations to find the other variable. You can also multiply one equation by a number to make the cancellation possible. For example, with 2x + 3y = 6 and 4x − y = 5, you can multiply the second equation by 3 to get 12x − 3y = 15, then add to the first to cancel y and obtain 14x = 21, so x = 3/2, and then y = 1. This method is especially efficient when you can create cancellation with minimal steps, which is why it’s a preferred approach for solving systems.

Eliminating a variable by adding the equations until one variable disappears is the idea here. You rewrite the system in standard form and align like terms so that the coefficients of one variable sum to zero. Then you add (or subtract) the equations to cancel that variable, leaving you with an equation in a single variable. After solving for that variable, you substitute back into one of the original equations to find the other variable. You can also multiply one equation by a number to make the cancellation possible. For example, with 2x + 3y = 6 and 4x − y = 5, you can multiply the second equation by 3 to get 12x − 3y = 15, then add to the first to cancel y and obtain 14x = 21, so x = 3/2, and then y = 1. This method is especially efficient when you can create cancellation with minimal steps, which is why it’s a preferred approach for solving systems.