To determine the best method for solving the given system of equations:
- \( 0.5x - 1.4y = 5.8 \)
- \( y = -0.3x - \frac{1}{5} \)
Let's analyze the methods:
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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.
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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.
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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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