Question

How do solve the following linear system?: `6x-4y=-1 , 3y = 15 -x`?

Answer 1

`x=57/22,y=91/22`

Explanation:

Writing the second equation in the form

`x=15-3y`
plugging this in the first equation

`6(15-3y)-4y=-1`
expanding we get

`90-18y-4y=-1`
substracting `90` and combining like Terms

`-22y=-91`
so
`y=91/22`

so
`x=15-3*91/22`

`x=(15*22-3*91)/22=57/22`

Answer 2

`x=57/22`, `y=91/22`

Explanation:

The given linear equations

`6x-4y=-1\ ..........(1)`

`3y=15-x`

or

`x+3y=15\ ..........(2)`

Multiplying (2) by `6` & subtracting from (1) as follows

`6x-4y-6(x+3y)=-1-6\times 15`

`-22y=-91`

`y=91/22`

setting `y=91/22` in (2), we get

`x=15-3y`

`=15-3(91/22)`

`=57/22`