Which statement correctly describes the algebraic elimination method as given?

Which statement correctly describes the algebraic elimination method as given?

• A. Substituting one equation into another to solve for a variable
• B. Graphing to find the intersection
• C. Adding or subtracting the same number to each equation to eliminate a variable
• D. Using the quadratic formula

Answer: (C)

The elimination process cancels one variable by combining the two equations so that that variable’s terms add to zero. You usually multiply one equation by a suitable number and then add or subtract the equations, leaving a single equation in the other variable. Once you solve for that variable, you back-substitute to find the remaining one. For example, with 2x + 3y = 6 and x − y = 1, multiply the second by 3 to get 3x − 3y = 3, then add to the first to eliminate y and solve for x, then back-substitute to find y. This is what the elimination method does: create a combination of the equations that removes a variable so you can solve step by step. Substitution, graphing, and the quadratic formula are different techniques for solving systems or equations and don’t describe the elimination process.

The elimination process cancels one variable by combining the two equations so that that variable’s terms add to zero. You usually multiply one equation by a suitable number and then add or subtract the equations, leaving a single equation in the other variable. Once you solve for that variable, you back-substitute to find the remaining one. For example, with 2x + 3y = 6 and x − y = 1, multiply the second by 3 to get 3x − 3y = 3, then add to the first to eliminate y and solve for x, then back-substitute to find y. This is what the elimination method does: create a combination of the equations that removes a variable so you can solve step by step. Substitution, graphing, and the quadratic formula are different techniques for solving systems or equations and don’t describe the elimination process.