To determine if \((-2, 6)\) is a solution to the system of linear equations \(x + 2y = 10\) and \(3x + y = 0\), we can substitute \(x = -2\) and \(y = 6\) into both equations and see if they hold true.
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For the first equation \(x + 2y = 10\): \[ -2 + 2(6) = -2 + 12 = 10 \quad \text{(True)} \]
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For the second equation \(3x + y = 0\): \[ 3(-2) + 6 = -6 + 6 = 0 \quad \text{(True)} \]
Since both equations are satisfied by the point \((-2, 6)\), it is indeed a solution to the system of equations.
Thus, the correct response is:
Yes, because the graphs intersect at (−2, 6).