3.) \( \begin{aligned} x & =9 y-24 \\ x & +7 y=24\end{aligned} \)
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Simplify this solution The Deep Dive
To solve this system of equations, we can substitute from the first equation into the second. We have \( x = 9y - 24 \). Now, substituting this into the second equation gives us: \[ (9y - 24) + 7y = 24 \] Combining like terms results in \( 16y - 24 = 24 \). Adding 24 to both sides yields \( 16y = 48 \), thus \( y = 3 \). Now, substituting \( y = 3 \) back into the first equation gives us: \[ x = 9(3) - 24 = 27 - 24 = 3 \] So, the solution to the system is \( (x, y) = (3, 3) \). Here's a quick tip: Always check your solutions by substituting back into the original equations to verify correctness. A common mistake is to overlook this step, resulting in incorrect confirmations of solutions!
