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To match the solutions with their system, we'll substitute the first point into the first system. If the point is a solution to both equations, it's a solution ot the system.
The equality is true for the second equation but not for the first one. A solution to a system of equations has to satisfy **all** equations. Therefore, $(8,4)$ cannot be a solution to the first system. Let's try the second point, $(4,6).$
Both equations are satisfied for $(4,6).$ Thus, it's a solution to the system. Continue with B and check with the first point.
It's a solution! This means that the last point must be a solution to the last system of equations. Let's find out.
We have now paired the three solutions with the three systems.
$A:B:C: (4,6)(8,4)(1,-3) $

${y−3x=-6y=-0.5x+8 $

${4−3⋅8=?-64=?-0.5⋅8+8 $

MultiplyMultiply

${4−24=?-64=?-4+8 $

AddSubTermsAdd and subtract terms

${-20 =-64=4 $

${y−3x=-6y=-0.5x+8 $

${6−3⋅4=?-66=?-0.5⋅4+8 $

MultiplyMultiply

${6−12=?-66=?-2+8 $

AddSubTermsAdd and subtract terms

${-6=-66=6 $

${y−20=-2xy−x+4=0 (I)(II) $

${4−20=?-2⋅84−8+4=?0 $

Multiply$(I):$Multiply

${4−20=?-164−8+4=?0 $

AddSubTermsAdd and subtract terms

${-16=-160=0 $

${y=2−5x7x−10=y (I)(II) $

${-3=?2−5⋅17⋅1−10=?-3 $

MultiplyMultiply

${-3=?2−57−10=?-3 $

SubTermsSubtract terms

${-3=-3-3=-3 $