In the substitution method for solving a system, what is the typical first step?

In the substitution method for solving a system, what is the typical first step?

• A. Solve one equation for one variable and substitute into the other
• B. Multiply equations to eliminate a variable
• C. Graph both equations and find intersection
• D. Add the equations

Answer: (A)

In the substitution method, you start by isolating one variable in one of the equations. This gives you an expression for that variable in terms of the other variable(s), which you can substitute into the other equation. By replacing the chosen variable with that expression, you turn the system into a single-variable equation you can solve, and then you back-substitute to find the remaining variable. For example, if you have x + y = 3 and 2x − y = 1, solve the first for y: y = 3 − x. Substitute into the second: 2x − (3 − x) = 1, which simplifies to 3x = 4, so x = 4/3 and then y = 3 − 4/3 = 5/3.

In the substitution method, you start by isolating one variable in one of the equations. This gives you an expression for that variable in terms of the other variable(s), which you can substitute into the other equation. By replacing the chosen variable with that expression, you turn the system into a single-variable equation you can solve, and then you back-substitute to find the remaining variable.

For example, if you have x + y = 3 and 2x − y = 1, solve the first for y: y = 3 − x. Substitute into the second: 2x − (3 − x) = 1, which simplifies to 3x = 4, so x = 4/3 and then y = 3 − 4/3 = 5/3.