Verified Answer :

7x+5y=-24 (1)
   4x+y=42 (2)

multiply equation (2) by 5 to get
20x+5y=210 (3)

then calculate (3)-(2) which gives you
13x=234 hence x=18
then substitute for x in either equation to get y=-30

{ 7x + 5y = - 24
{ 4x + y = 42    ⇒  y = 42 - 4x

7x + 5y = - 24
7x + 5.( 42 - 4x ) = - 24
7x + 210 - 20x = - 24
7x - 20x = - 24 - 210
- 13x = - 234 .(-1)
  13x = 234
   x = 234
          13
   x = 18

4x + y = 42
4.(18) + y = 42
72 + y = 42
y = 42 - 72
y = - 30

S = { 18 , - 30 }

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