Question
Which would be the best method to solve this system?
2x+3y=15
x-3y=3
*
1 point
Elimination
Substitution
Graphing
2x+3y=15
x-3y=3
*
1 point
Elimination
Substitution
Graphing
Answers
GPT-4o mini
To determine the best method to solve the system of equations given:
1. \(2x + 3y = 15\)
2. \(x - 3y = 3\)
let's analyze the options:
1. **Elimination**: This method involves adding or subtracting the equations to eliminate one of the variables. Given that the coefficients of \(y\) in the first equation (3) and the second equation (-3) have the same magnitude but opposite signs, this method could work well and be straightforward.
2. **Substitution**: This method substitutes one variable in terms of the other using one equation and then replaces it in the second equation. It is also a feasible method, especially if one equation is easily solvable for one variable.
3. **Graphing**: This method involves plotting both equations on a graph and finding the intersection point. While it is a valid approach, it can be less precise and more time-consuming than algebraic methods, especially for determining the exact solution.
Considering all these factors, the **elimination method** would likely be the most efficient for this specific system, as it's straightforward to see how the coefficients can be manipulated to eliminate one of the variables directly.
Thus, the best method to solve this system is **Elimination**.
1. \(2x + 3y = 15\)
2. \(x - 3y = 3\)
let's analyze the options:
1. **Elimination**: This method involves adding or subtracting the equations to eliminate one of the variables. Given that the coefficients of \(y\) in the first equation (3) and the second equation (-3) have the same magnitude but opposite signs, this method could work well and be straightforward.
2. **Substitution**: This method substitutes one variable in terms of the other using one equation and then replaces it in the second equation. It is also a feasible method, especially if one equation is easily solvable for one variable.
3. **Graphing**: This method involves plotting both equations on a graph and finding the intersection point. While it is a valid approach, it can be less precise and more time-consuming than algebraic methods, especially for determining the exact solution.
Considering all these factors, the **elimination method** would likely be the most efficient for this specific system, as it's straightforward to see how the coefficients can be manipulated to eliminate one of the variables directly.
Thus, the best method to solve this system is **Elimination**.