Question

Which is the best first step when solving the following system of equations?

A.) Multiply the first equation by 4.
B.) Add the first equation to the second equation.
C.) Multiply the second equation by -1.
D.) Subtract the second equation from the first equation.

Answer 1

The best first step for solving a system of equations is typically to add or subtract the equations or to multiply one by a number to align the coefficients, which simplifies the system.

Step-by-step explanation:

To determine the best first step when solving the system of equations, we must consider the specifics of the system which are not provided here. However, in general, adding or subtracting equations is a common starting point that simplifies the system. Multiplying an equation by a number is also a valid approach, especially if it makes the coefficients of one variable the same (or opposite) so that adding or subtracting the equations would eliminate one variable.

For example, in systems of the form \(y = mx + b\), like those mentioned in the Practice Test 4 Solutions, if one equation is multiplied by a factor that allows the \(y\) coefficients to become opposites, the addition or subtraction of the equations will easily eliminate \(y\), simplifying the process. It's important to choose a method that minimizes the complexity and the potential for errors, keeping in mind that some systems may require more than one step or related keywords to solve.