Question

1/3 x− 1/8 y=3
7y+9x=−2
please solve the system
45 points for who does

Answer 1

`x=6\\y=-8`

Explanation:

`(1)/(3)x-(1)/(8)y=3\\ 7y+9x=-2`

One method could be rewriting the second equation as x in terms of y and solving by replacing in the first equation.

`7y+9x=-2\\9x=-2-7y\\x=(-7y-2)/(9)`

Replace...

`(1)/(3)x-(1)/(8)y=3`

`(1)/(3)((-7y-2)/(9))-(1)/(8)y=3`

`(-7y-2)/(27)-(1)/(8)y=3`

`-(7)/(27)y-(2)/(27)-(1)/(8)y=3`

add
`(2)/(27)` on both sides.

`-(7)/(27)y-(1)/(8)y=3+(2)/(27)`

Combine like terms

`((-7)(8)-(1)(27))/((27)(8)) y=((3)(27)+2)/(27)`

`(-56-27)/(216) y=(81+2)/(27)`

`(-83)/(216)y =(83)/(27)`

Now, to get rid of the fraction and isolate y, multiply by the reciprocal or the inverted fraction.

`((216)/(-83)) (-83)/(216)y =(83)/(27)((216)/(-83))`

`y=(216)/(-27)`

Simplify

`y=-8`

Now replace the value of y in either equation to find x.

`7y+9x=-2\\7(-8)+9x=-2\\-56+9x=-2`

add 56

`56-56+9x=-2+56\\9x=54\\`

Divide by 9

`(9x)/(9)=(54)/(9)\\ x=6`

To check whether these values are accurate, replace in either equation both values and you should have an equality. In this case I'll do it in both equations.

`(1)/(3)x-(1)/(8)y=3`

`(1)/(3)(6)-(1)/(8)(-8)=3`

`2-(-1)=3\\2+1=3\\3=3`

-----------------------------------------------------------------

`7y+9x=-2\\7(-8)+9(6)=-2\\-56+54=-2\\-2=-2`