Question

5x - 10y = 15 if 3x + 7y = 31

Answer 1

5x - 10y = 15...reduces to x - 2y = 3
3x + 7y = 31

x - 2y = 3....multiply by -3
3x + 7y = 31
---------------
-3x + 6y = -9 (result of multiplying by -3)
3x + 7y = 31
---------------add
13y = 22
y = 22/13

x - 2y = 3
x - 2(22/13) = 3
x - 44/13 = 3
x = 3 + 44/13
x = 39/13 + 44/13
x = 83/13

solution is (83/13, 22/13) <=

Answer 2

3(5x-10y=15)-5(3x+7y=31)

15x-30y-15x-35y=45-155

-65y=-110

y=22/13, making 3x+7y=31 become

3x+154/13=31

39x+154=403

39x=249

x=83/13

So the solution to the system of equation is the point (83/13, 22/13)