To solve the given system of equations:
- \( y = 5x - 2 \)
- \( 2x + 9y = 10 \)
let's analyze the methods:
A. Graphing: While graphing can provide a visual representation of the solution, it may not be very precise unless done with a graphing tool. It can be time-consuming as well.
B. Substitution: Since the first equation is already solved for \( y \), we can substitute \( y \) from the first equation into the second equation. This is often efficient when one equation is already solved for one variable.
C. Elimination: This method involves manipulating the equations to eliminate one of the variables. While effective, it often requires more steps than substitution in this case.
Given that we can directly substitute \( y \) from the first equation into the second, the most efficient method here is B. Substitution.
Let's demonstrate the substitution method:
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Substitute \( y = 5x - 2 \) into the second equation: \( 2x + 9(5x - 2) = 10 \)
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Expand and simplify: \( 2x + 45x - 18 = 10 \) \( 47x - 18 = 10 \)
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Solve for \( x \): \( 47x = 28 \) \( x = \frac{28}{47} \)
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Substitute \( x \) back into the first equation to find \( y \): \( y = 5\left(\frac{28}{47}\right) - 2 \) \( y = \frac{140}{47} - 2 = \frac{140}{47} - \frac{94}{47} = \frac{46}{47} \)
Thus, the solution is \( x = \frac{28}{47}, y = \frac{46}{47} \).
So, the final answer is B. Substitution.
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