Which sequence describes solving systems by substitution?

Which sequence describes solving systems by substitution?

• A. Solve one equation for x or y; plug into the other; solve for the remaining variable; substitute back
• B. Multiply both equations by a suitable number to align coefficients
• C. Graph both equations and determine the intersection
• D. Solve for one variable, then set equal to the other equation

Answer: (C)

Substitution works by replacing one variable with an expression from the other equation. Start by solving one equation for x or y. Then take that expression and substitute it into the other equation, which gives you a single equation in one variable. Solve for that variable, and finally plug that value back into either original equation to find the other variable. This approach gives an exact solution using algebraic replacement. The graphing description describes a different method: you plot both lines and find their intersection, which can be approximate. The multiplication step describes the elimination method, another distinct technique. The idea of solving for one variable and then “setting it equal” to the other equation doesn’t complete the substitution process, since it doesn’t involve substituting that expression into the other equation.

Substitution works by replacing one variable with an expression from the other equation. Start by solving one equation for x or y. Then take that expression and substitute it into the other equation, which gives you a single equation in one variable. Solve for that variable, and finally plug that value back into either original equation to find the other variable. This approach gives an exact solution using algebraic replacement.

The graphing description describes a different method: you plot both lines and find their intersection, which can be approximate. The multiplication step describes the elimination method, another distinct technique. The idea of solving for one variable and then “setting it equal” to the other equation doesn’t complete the substitution process, since it doesn’t involve substituting that expression into the other equation.