There are several different methods to solve systems of equations.
Notice that each of these equations can be put into a simpler form by dividing each term by a common factor.
#7x +7y = 28 ..............................div 7#
#x + y = 4#
#color(red)(y = 4-x)" "larr # A
#10x +2y = -8...........................div 2#
#5x +y = -4#
#color(blue)(y = -4-5x)" "larr # B
Now each equation A and B has #y# as the subject
#color(white)(xxxxxxxxxxxxxx)color(red)(y)=color(blue)(y)#
#color(white)(xxxxxxxxxxx)color(red)(4-x)=color(blue)(-4-5x)" "larr# solve for x
#color(white)(xxxxxxxxxx)5x-x=-4-4#
#color(white)(xxxxxxxxxxxxx)4x=-8#
#color(white)(xxxxxxxxxxxx.x)x=-2#
Now substitute for #x# in A and B.
#color(red)(y = 4-(-2))" "larr # A
#color(red)(y = 6)#
#color(blue)(y = -4-5(-2))" "larr # B
#color(blue)(y = -4+10)#
#color(blue)(y = 6#
Both equations give the same result for #y#.
The values are correct.
#x = -2 and y = 6#
