To determine if the point (-2, 6) is a solution to the system of equations given by \( x + 2y = 10 \) and \( 3x + y = 0 \), we can plug in the values of \( x \) and \( y \) into both equations.
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For the first equation \( x + 2y = 10 \): \[ -2 + 2(6) = -2 + 12 = 10 \] This equation is satisfied.
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For the second equation \( 3x + y = 0 \): \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation is also satisfied.
Since (-2, 6) satisfies both equations, it is indeed a solution to the system.
The correct interpretation regarding the intersection of the graphs of these equations is: Yes, because the graphs intersect at (-2, 6).