Question

Which method would be the most efficient to solve the system? (1 point)

1
y= -x
2x + 3y = 28
graphing
substitution
elimination
●distributive

Answer 1

[AI-generated answer — Bot]

elimination

Answer 2

I prefer substitution, since you have y = -x already to use.

Answer 3

[AI-generated answer — Bot]

That is a valid approach too! Substitution would also work well in this case since you can substitute y = -x into the second equation and get 2x + 3(-x) = 28. Then you can solve for x and plug the value back into one of the original equations to find y.

Answer 4

[AI-generated answer — Explain Bot]

To determine the most efficient method for solving the given system of equations, we need to consider the options: graphing, substitution, elimination, and distributive.

1. Graphing: This method involves graphing both equations on a coordinate plane and finding the point(s) where they intersect. However, this can be time-consuming and less accurate compared to other methods. It is not the most efficient method for solving this system.

2. Substitution: In this method, we solve one equation for one variable and then substitute that expression into the other equation. This eliminates one variable, allowing us to solve for the remaining variable. While this method can work for any system, it may involve more steps in this particular instance. So, it may not be the most efficient method.

3. Elimination: In this method, we manipulate the equations by adding or subtracting them in a way that eliminates one variable. This creates a simpler equation with only one variable, which can then be easily solved. Elimination can be a more efficient method for solving the given system since one of the equations is already in terms of y. We can multiply the first equation by 3, giving us -3x + 3y = 0. By adding this equation to the second equation, the y-terms will cancel out, and we can solve for x. Once we have x, we can substitute it back into one of the original equations to solve for y.

4. Distributive: The term "distributive" typically refers to a property of multiplication over addition or subtraction. It is not a method for solving systems of linear equations. Therefore, this option is not applicable for solving the given system.

In conclusion, the most efficient method for solving the given system would be elimination.