Question

In two or more complete sentences, describe a system of equations in which subtraction would be the most efficient way of solving the system.

Answer 1

Let us suppose a system of two equations with two unknowns.

Suppose further that the system of equations is linearly independent.

When the system of equations has a variable that has exactly the same coefficient in both equations, then the most effective method to solve the system of equations is subtracting.

This is because we eliminate one of the variables and reduce the system to an equation with one unknown.

Answer:

a system of equations in which subtraction would be the most efficient way of solving the system is:

A system of equations in which one of the variables has exactly the same coefficient in both equations.

Answer 2

In subtraction method, the 2 equations in the system are subtracted to form a new equation with only 1 variable. To work out for the new equation to have only 1 variable, the other variable must be canceled out. In other words, we must  perform operations on each equation first until 1 term has an equal and opposite coefficient as the corresponding term in the other equation.