What is solution 7x+5y=-24 and 4x+y=42?

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 }