To determine if the point \((-2, 6)\) is a solution to the system of equations \(x + 2y = 10\) and \(3x + y = 0\), we need to substitute \(x = -2\) and \(y = 6\) into both equations and check if they hold true.
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Checking the first equation \(x + 2y = 10\):
\[ -2 + 2(6) = -2 + 12 = 10 \]
The first equation is satisfied.
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Checking the second equation \(3x + y = 0\):
\[ 3(-2) + 6 = -6 + 6 = 0 \]
The second equation is also satisfied.
Since both equations are satisfied, \((-2, 6)\) is indeed a solution to the system of equations.
The correct answer is:
Yes, because the graphs intersect at \((-2, 6)\).