Six times a number x, plus 4 times a number y, equals 14. negative eight times x minus 4 times y equals -12. what are the numbers?

Converting this into an equation, we get:
6x+4y=14
-8x-4y=-12

We can solve this by adding the system of equations.

       6x+4y=14
 +   -8x-4y=-12

      -2x=2

Simplifying, we get that x=-1. We can replug this into one of the equations to get y. We'll choose 6x+4y=14

Plugging in -1 for x, we get that:
6(-1)+4y=14
which is
-6+4y=14
which is
4y=20

Simplify this to get that y=5

To check, you can plug in x and y into both equations to make sure that they are true.

6(-1)+4(5)=14
-6+20=14
14=14 which is true

-8(-1)-4(5)=-12
8-20=-12
-12=-12 which is true

x=-1 and y=5

:)

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.