Question

How do you solve `5x+2y=12` and `-6x-2y=-14`?

Answer 1

`{(x=2),(y=1):}`

Explanation:

`{(5x+2y=12" S1"),(-6x-2y=-14" S2"):}`

Looking at the equation we can see that in `S1` we have `ay` and in `S2` we have `-ay`, thus we could use the Linear Systems with Addition or Subtraction to transform the system as :

`{(S1),(S1+S2):}`

`{(5x+2y=12),(-x+0y=-2):}=>{(5x+2y=12),(x=2):}`

Now you can put the `x` value in `S1` to find the `y` value

`{(5*2+2y=12),(x=2):}=>{(10+2y=12),(x=2):}=>{(5x+2y=12),(x=2):}`

`=>{(2y=12-10),(x=2):}=>{(y=cancel(2)^1/cancel(2)^1),(x=2):}`

`=>{(x=2),(y=1):}`

graph{(5x+2y-12)(-6x-2y+14)=0 [-1.413, 5.518, -1.016, 2.45]}