Question

Write a system of linear equations that could be solved easily by substitution. Write a system of linear equations that could not be solved easily by substitution. Explain your reasoning.

Answer 1

A system with one equation solved for a variable is easy for substitution, like y = 2x + 3 and 3y - 6x = 12. A system with proportional standard form equations like 2x + 3y = 6 and 4x + 6y = 12 is not ideal for substitution.

Step-by-step explanation:

To create a system of linear equations that can be easily solved by substitution, one of the equations should be solved for one variable. For instance:

• Equation 1: y = 2x + 3
• Equation 2: 3y - 6x = 12

Here, you can directly substitute the expression for y from Equation 1 into Equation 2.

However, a system that is not easily solved by substitution might involve equations where both are expressed in a standard form that does not isolate one variable, like:

• Equation 1: 2x + 3y = 6
• Equation 2: 4x + 6y = 12

For these equations, neither variable is isolated, and they are proportional, making substitution less straightforward. In this case, methods such as elimination might be more suitable.