Question

Write a system of equations for which the best method of solving is substitution. Explain why substitution works best for this system.

Answer 1

Substitution is a method used to solve systems of equations. It works best when one equation can be solved for a variable, and then that expression is substituted into the other equation(s).

Step-by-step explanation:

Substitution is a method used to solve systems of equations. It works best when one equation can be solved for a variable, and then that expression is substituted into the other equation(s).

For example, let's say we have the following system of equations:

Equation 1: 2x + 3y = 9

Equation 2: x - y = 1

We can solve Equation 2 for x to get x = y + 1. Then, we substitute this expression into Equation 1:

2(y + 1) + 3y = 9

Simplifying, we get 2y + 2 + 3y = 9.

Combining like terms, we have 5y + 2 = 9.

Finally, we solve for y to get y = 7/5. Substituting this value back into x = y + 1, we find x = 12/5.

So the solution to the system of equations is x = 12/5 and y = 7/5.