Asked by sam.
which method would be best to solve this system
0.5x - 1.4y = 5.8
y= -0.3x - 1/5
Graphing
substitution
elimination
0.5x - 1.4y = 5.8
y= -0.3x - 1/5
Graphing
substitution
elimination
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the best method for solving the given system of equations:
1. \( 0.5x - 1.4y = 5.8 \)
2. \( y = -0.3x - \frac{1}{5} \)
Let's analyze the methods:
1. **Graphing**: This method involves plotting both equations on a graph to find the intersection point. While it's visually intuitive, it may not provide an exact solution unless the intersection is clear and accurately plotted. It can be time-consuming for more complicated equations.
2. **Substitution**: Since the second equation is already solved for \(y\), substitution could be straightforward. You can substitute the expression for \(y\) from the second equation into the first equation, which would allow you to solve for \(x\) first.
3. **Elimination**: This method involves manipulating the equations to eliminate one variable. This could be effective but may require more steps to align the equations for elimination.
Given that the second equation is already in the form of \(y = \text{expression}\), **substitution** is likely the most efficient method for this system. You can directly substitute the expression for \(y\) into the first equation and solve for \(x\) easily.
Thus, I recommend using the **substitution method** to solve the system.
1. \( 0.5x - 1.4y = 5.8 \)
2. \( y = -0.3x - \frac{1}{5} \)
Let's analyze the methods:
1. **Graphing**: This method involves plotting both equations on a graph to find the intersection point. While it's visually intuitive, it may not provide an exact solution unless the intersection is clear and accurately plotted. It can be time-consuming for more complicated equations.
2. **Substitution**: Since the second equation is already solved for \(y\), substitution could be straightforward. You can substitute the expression for \(y\) from the second equation into the first equation, which would allow you to solve for \(x\) first.
3. **Elimination**: This method involves manipulating the equations to eliminate one variable. This could be effective but may require more steps to align the equations for elimination.
Given that the second equation is already in the form of \(y = \text{expression}\), **substitution** is likely the most efficient method for this system. You can directly substitute the expression for \(y\) into the first equation and solve for \(x\) easily.
Thus, I recommend using the **substitution method** to solve the system.
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