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Question 7 of 10 If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation? \( 2 x+6 y=9 \) \( 3 x-12 y=15 \) A. \( x \), in the first equation B. \( y \), in the first equation C. \( x \), in the second equation D. \( y \), in the second equation SUBMIT

Ask by Goodwin Young. in the United States
Feb 26,2025

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Solve for \(x\) in the first equation.

Solución

To solve the system of equations by substitution, we need to choose a variable to solve for and an equation to use for substitution. Given equations: 1. \(2x + 6y = 9\) 2. \(3x - 12y = 15\) Let's analyze the options provided: A. Solving for \(x\) in the first equation: \(2x + 6y = 9\) \(2x = 9 - 6y\) \(x = \frac{9 - 6y}{2}\) B. Solving for \(y\) in the first equation: \(2x + 6y = 9\) \(6y = 9 - 2x\) \(y = \frac{9 - 2x}{6}\) C. Solving for \(x\) in the second equation: \(3x - 12y = 15\) \(3x = 15 + 12y\) \(x = \frac{15 + 12y}{3}\) D. Solving for \(y\) in the second equation: \(3x - 12y = 15\) \(-12y = 15 - 3x\) \(y = \frac{15 - 3x}{-12}\) Based on the options provided, the best variable to solve for and from which equation would be: A. Solving for \(x\) in the first equation.

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Extra Insights

To solve the system using substitution, let's take a closer look at the equations. The first equation, \(2x + 6y = 9\), can be simplified to make it easier to isolate a variable. Solving for \(y\) from this equation is quite straightforward, as it allows us to avoid dealing with fractions right away. So, picking option B, \(y\) in the first equation, keeps things simple! Now let's talk about how choosing the right variable can save you time and frustration. If you note the coefficients in the equations, \(y\) in the first has a nice integer to work with (6), while in the second equation, the \(y\) term is -12. Choosing to isolate \(y\) in the first equation boosts your efficiency in solving!

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