Which statement describes the algebraic elimination method?

Which statement describes the algebraic elimination method?

• A. Substituting one equation into another
• B. Graphing the system 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)

Canceling a variable by forming a linear combination of the equations so that one variable disappears is what the algebraic elimination method is all about. You adjust the equations—usually by multiplying one equation by a number—so that the coefficients of a chosen variable are equal in magnitude and opposite in sign. Then you add or subtract the equations to eliminate that variable, leaving an equation with a single variable to solve. After finding that variable, you substitute back into one of the original equations to get the other. For example, with two linear equations, you can multiply one equation by a number to create opposite coefficients for a variable, add the equations to cancel that variable, solve the remaining equation, then back-substitute to find the other variable. This method is a structured way to turn a two-variable system into a single-variable equation. Other approaches described by the remaining options include graphing the system to locate where the lines intersect, which finds the solution point geometrically; substituting one equation into the other, which uses solving one equation for a variable and plugging it into the second; and using the quadratic formula, which solves single-variable quadratic equations rather than a linear system.

Canceling a variable by forming a linear combination of the equations so that one variable disappears is what the algebraic elimination method is all about. You adjust the equations—usually by multiplying one equation by a number—so that the coefficients of a chosen variable are equal in magnitude and opposite in sign. Then you add or subtract the equations to eliminate that variable, leaving an equation with a single variable to solve. After finding that variable, you substitute back into one of the original equations to get the other.

For example, with two linear equations, you can multiply one equation by a number to create opposite coefficients for a variable, add the equations to cancel that variable, solve the remaining equation, then back-substitute to find the other variable. This method is a structured way to turn a two-variable system into a single-variable equation.

Other approaches described by the remaining options include graphing the system to locate where the lines intersect, which finds the solution point geometrically; substituting one equation into the other, which uses solving one equation for a variable and plugging it into the second; and using the quadratic formula, which solves single-variable quadratic equations rather than a linear system.