Question

How do you determine the solution in terms of a system of linear equations for `-5x-5y=5`, `-40x-3y=2`?

Answer 1

`x=1/37` and `y=-38/37`

Explanation:

`-5x-5y=5`
`-40x-3y=2`

Lets cancel out the `y` terms to find `x`. Multiply the top equation by `-3` and the bottom equation by `-5` (multiply equations by opposite coefficients of `y`):

`(-5x*-3)-(5y*-3)=5*-3`
`(-40x*-5)-(3y*-5)=2*-5`

`15x+15y=-15`
`200x+15y=-10`

Subtract them from each other to eliminate `y`:

`-185x= -5`
`x=-5/-185`
`x=1/37`

Substitute `x=1/37` back into one of the original equations (e.g. `-5x-5y=5`) to find `y`:

`-5(1/37)-5y=5`
`(-5/37)-5y=5`
`-5y=5+(5/37)`
`-5y=190/37`
`y=(190/37)/-5`
`y=-38/37`

Double check your results by substituting both values of `x` and `y` into an original equation and see whether the result is correct.