What is typically the first step in solving by substitution?

What is typically the first step in solving by substitution?

• A. Graph both equations
• B. Multiply equations to align coefficients
• C. Solve for one variable
• D. Solve one equation for x or y

Answer: (D)

In solving systems by substitution, you want to replace a variable with an expression in terms of the other variable. The first move is to isolate one variable in one equation, solving for x or for y. This gives you an expression to plug into the other equation, turning the system into a single-variable equation to solve. For example, from an equation like 4x + 2y = 8, solve for x: x = 2 - (1/2)y. Now you can substitute that expression for x into the other equation, solve for y, and then back-substitute to find x. This approach makes it possible to work with just one variable at a time. Other strategies, like graphing both equations or multiplying to align coefficients, are used in different methods (graphical or elimination) and aren’t the typical first step for the substitution method.

In solving systems by substitution, you want to replace a variable with an expression in terms of the other variable. The first move is to isolate one variable in one equation, solving for x or for y. This gives you an expression to plug into the other equation, turning the system into a single-variable equation to solve.

For example, from an equation like 4x + 2y = 8, solve for x: x = 2 - (1/2)y. Now you can substitute that expression for x into the other equation, solve for y, and then back-substitute to find x. This approach makes it possible to work with just one variable at a time.

Other strategies, like graphing both equations or multiplying to align coefficients, are used in different methods (graphical or elimination) and aren’t the typical first step for the substitution method.