Which method involves adding equations to eliminate a variable in a system?

Which method involves adding equations to eliminate a variable in a system?

• A. Addition/subtraction method
• B. Substitution method
• C. Graphical method
• D. Factoring method

Answer: (A)

Elimination method. When solving a system of linear equations, you cancel one variable by adding or subtracting equations after adjusting them so the coefficients of that variable are opposites. This gives a new equation with only one variable, which you can solve, then back-substitute to find the other variable. For example, with 2x + 3y = 5 and 4x − y = 1, multiply the second equation by 3 to get 12x − 3y = 3, then add to the first equation to eliminate y: (2x + 3y) + (12x − 3y) = 5 + 3, yielding 14x = 8, so x = 4/7, and you can substitute back to find y. The core idea is using addition (or subtraction) of equations to cancel a variable, which is why this method is described as the elimination approach. Other methods exist for solving systems: the substitution method solves one equation for a variable and substitutes into the other, the graphical method relies on the intersection point of the graphs, and the factoring approach isn’t typically used for general linear systems.

Elimination method. When solving a system of linear equations, you cancel one variable by adding or subtracting equations after adjusting them so the coefficients of that variable are opposites. This gives a new equation with only one variable, which you can solve, then back-substitute to find the other variable. For example, with 2x + 3y = 5 and 4x − y = 1, multiply the second equation by 3 to get 12x − 3y = 3, then add to the first equation to eliminate y: (2x + 3y) + (12x − 3y) = 5 + 3, yielding 14x = 8, so x = 4/7, and you can substitute back to find y. The core idea is using addition (or subtraction) of equations to cancel a variable, which is why this method is described as the elimination approach.

Other methods exist for solving systems: the substitution method solves one equation for a variable and substitutes into the other, the graphical method relies on the intersection point of the graphs, and the factoring approach isn’t typically used for general linear systems.