Question

How can we get system [b] from system [a]? Choose 1 answer:

1) Replace only the right-hand side of one equation with the sum/difference of the right-hand sides of both equations
2) Replace one equation with the sum/difference of both equations
3) Swap only the left-hand sides of both equations
4) Swap the order of the equations

Answer 1

To transform system [a] into system [b], choose option (2), which involves replacing one equation with the sum/difference of both equations, a method used to simplify or solve systems of equations by eliminating one of the variables.

Step-by-step explanation:

To get system [b] from system [a], the correct answer is option 2) Replace one equation with the sum/difference of both equations. This is a common technique used to manipulate systems of equations, which allows us to combine the information from both equations into a single equation that may be easier to solve or can be used in conjunction with another equation to find the solution to the system.

When we 'replace one equation with the sum/difference of both equations', we are typically trying to eliminate one variable, in order to solve for the other. An example of using this technique is seen when we have two equations such as:

• Equation 1: x + y = 5
• Equation 2: x - y = 1

If we add these two equations together, y is eliminated, and we get 2x = 6. This can then be used to solve for x.