Question

what is the first step when using the substitution method?

multiply both equations by a constant
solve one equation for a variable
graph both equations
add the equations together

Explanation:

Identify the goal of the substitution method

Using the Substitution Method knowledge point
The goal of this method is to solve a system of equations by replacing one variable with an equivalent expression in terms of the other variable.

Determine the initial step

Using the Substitution Method knowledge point
To substitute one variable into another equation, we must first isolate that variable. Therefore, the first step is to solve one of the equations for either \(x\) or \(y\).

Analyze the given options

Using the Substitution Method knowledge point

• "Multiply both equations by a constant": This is typically used in the elimination method.
• "Solve one equation for a variable": This is the correct first step to allow substitution.
• "Graph both equations": This is used in the graphical method.
• "Add the equations together": This is used in the elimination method.

Answer:

• Multiply both equations by a constant
• Solve one equation for a variable (Correct answer)
• Graph both equations
• Add the equations together