To use the elimination method, Tatum needs to make the coefficients of one of the variables (either \(x\) or \(y\)) the same in both equations. Let's look at the given system of equations:
- \(6x + 3y = 14\)
- \(3x + 2y = 10\)
To eliminate \(y\), we can aim to make the coefficients of \(y\) in both equations equal. The coefficients of \(y\) are \(3\) in the first equation and \(2\) in the second equation.
The least common multiple (LCM) of \(3\) and \(2\) is \(6\). Therefore, we want the \(y\)-terms to both be \(6\).
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To make the coefficient of \(y\) in the first equation equal to \(6\), you can multiply the entire first equation by \(2\): \[ 2(6x + 3y) = 2(14) \implies 12x + 6y = 28 \]
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To make the coefficient of \(y\) in the second equation equal to \(6\), you can multiply the entire second equation by \(3\): \[ 3(3x + 2y) = 3(10) \implies 9x + 6y = 30 \]
Now the system is:
- \(12x + 6y = 28\) (after multiplying the first equation by \(2\))
- \(9x + 6y = 30\) (after multiplying the second equation by \(3\))
Now, \(6y\) is the same in both equations, and you can subtract one equation from the other to eliminate \(y\).
Thus, Tatum should multiply the second equation by \(3\).
None of the given responses (−12, −1/2, 6622, −2) is correct, as they don't specify multiplying by \(3\). If you had to choose from the provided options based on closest mathematical approach for elimination, please check the options again.
However, the correct multiplying factor for the second equation to eliminate \(y\) is indeed \(3\).