In the elimination method, which statement describes the typical first step?

In the elimination method, which statement describes the typical first step?

• A. Solve for one variable and substitute into the other
• B. Line up terms in both equations; make coefficients opposite; add to eliminate; solve; substitute back
• C. Graph both equations and find the intersection
• D. Multiply one equation by a nonzero scalar only

Answer: (B)

Elimination is about canceling one variable so you can solve for the other. The typical first move is to line up the two equations so like terms line up, then adjust the coefficients so that one variable has opposite signs in the two equations. When you add the equations, that variable cancels, giving a single-variable equation you can solve. After you find that value, substitute it back into one of the original equations to get the other variable. This approach is different from substitution, where you solve for one variable and plug it into the other equation. It’s also not about graphing, which finds the solution at the intersection of the graphs. And while multiplying an equation by a nonzero scalar can help prepare for elimination, on its own it doesn’t eliminate a variable—the key is choosing coefficients so adding the equations removes one variable.

Elimination is about canceling one variable so you can solve for the other. The typical first move is to line up the two equations so like terms line up, then adjust the coefficients so that one variable has opposite signs in the two equations. When you add the equations, that variable cancels, giving a single-variable equation you can solve. After you find that value, substitute it back into one of the original equations to get the other variable.

This approach is different from substitution, where you solve for one variable and plug it into the other equation. It’s also not about graphing, which finds the solution at the intersection of the graphs. And while multiplying an equation by a nonzero scalar can help prepare for elimination, on its own it doesn’t eliminate a variable—the key is choosing coefficients so adding the equations removes one variable.