To determine if (−2, 6) is a solution to the system of equations:
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Substitute \( x = -2 \) and \( y = 6 \) into the first equation:
\( x + 2y = 10 \)
\(-2 + 2(6) = -2 + 12 = 10.\)
This equation is satisfied.
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Now substitute \( x = -2 \) and \( y = 6 \) into the second equation:
\( 3x + y = 0 \)
\( 3(-2) + 6 = -6 + 6 = 0.\)
This equation is also satisfied.
Since both equations are true with these values of \( x \) and \( y \), (−2, 6) is indeed a solution to the system of equations.
So the correct response is: Yes, because the graphs intersect at (−2, 6).