Question

How do you solve the system by graphing `x - 5y = -14` and `3x + y = 6`?

Answer 1

See explanantion

Explanation:

Given:
`x-5y=-14`........................(1)
`3x+y=6`..........................(2)

`color(blue)("Consider equation (1)")`

Multiply throughout by (-1)
`-x+5y=14`

Add `x` to both sides

`-x+x+5y=14+x`

`0+5y=x+14`

Divide both sides by 5

`5/5xxy=x/5+14/5`

But `5/5=1`

`color(blue)(y=x/5+14/5)`.......................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider equation (2)")`

By the same processes as above we end up with:

`color(blue)(y=-3x+6)`.........................(4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Plotting equations (3) and (4) we have: