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Reasoning Solve the system of linear equations using substitution. Use pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning: \( \begin{array}{l}x=3 y-9 \\ x+3 y=7\end{array} \) The solution is (Simplity your answer. Type an ordered pair.)

Ask by Hilton Craig. in the United States
Dec 07,2024

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(-1, 8/3)

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To solve the system of equations using substitution, we notice that the first equation \( x = 3y - 9 \) already expresses \( x \) in terms of \( y \). This makes it easier to substitute this expression for \( x \) into the second equation \( x + 3y = 7 \). By doing this, we can solve for \( y \) directly. Now, substituting \( x = 3y - 9 \) into the second equation gives us: \[ (3y - 9) + 3y = 7 \] Combine like terms: \[ 6y - 9 = 7 \] Adding 9 to both sides results in: \[ 6y = 16 \] Dividing both sides by 6 yields: \[ y = \frac{16}{6} = \frac{8}{3} \] Now, substitute \( y = \frac{8}{3} \) back into the first equation to find \( x \): \[ x = 3\left(\frac{8}{3}\right) - 9 \] Simplifying gives: \[ x = 8 - 9 = -1 \] Therefore, the solution to the system is \( (-1, \frac{8}{3}) \).

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