Question

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

x + y = 3

4x - y = 7

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 is to add the two equations, efficiently eliminating the y variable and leaving an equation with only x to solve for.

Step-by-step explanation:

The best first step when solving the system of equations x + y = 3 and 4x - y = 7 is to add the first equation to the second equation. This approach is quick and efficient as it eliminates the variable y immediately, and you're left with an equation containing only x. Once x is found, you can substitute it back into any of the original equations to solve for y.

Such a method falls under the category of elimination, which is often used to solve simultaneous equations. It simplifies the process and takes you one step closer to finding the solution for the unknowns.