Question

Question #498a4

Answer 1

`y=-9/5`
`x= 15`

Explanation:

The most straight forward way to resolve this particular is to get rid of the fraction as a first step.

`1/5x+y=6/5" ".................Equation(1)`
`1/10x+1/3y=9/10" "..........Equation(2)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider Eqn(1)")`

`color(green)([x/5]color(white)("d")+color(white)("d")[ycolor(red)(xx1)]color(white)("d")=[6/5])`

`color(green)([x/5]color(white)("d")+color(white)("d")[ycolor(red)(xx5/5)]color(white)("d")=[6/5])`

`x/5+(5y)/5=6/5`

Multiply both sides by 5

`x+5y=6" "......................Equation(1_a)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Consider Eqn(2)")`

`color(green)([x/10color(red)(xx1)]+[y/3color(red)(xx1)]=[9/10color(red)(xx1)] )`

`color(green)([x/10color(red)(xx3/3)]+[y/3color(red)(xx10/10)]=[9/10color(red)(xx3/3)] )`

`(3x)/30+(10y)/30=27/30`

Multiply both sides by 30

`3x+10y=27" "...........Equation(2_a)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`x+5y=6" "..................Eqn(1_a)`
`3x+10y=27" "............Eqn(2_a)`

`Eqn(2_a) -(3xxEqn(1_a))`

`3x+10y=27" "larr" "Eqn(2_a)`
`ul(3x+15y=18)" "larr" "3xxEqn(1_a)`
`0x-color(white)(2)5y=9`

Multiply both sides by (-1)

`+5y=-9`

Divide both sides by 5

`y=-9/5" ".............Eqn(3)`

I choose `Eqn(1_a)` it is works out more easily. You would still get the same answer if you used `Eqn(2_a)` but it would involve more work.

Using `Eqn(3)` substitute for `y` in `Eqn(1_a)`

`color(green)(x+5color(red)(y)=6" "->" "x+(5color(red)(xx-9/5))=6`

`x-9=6`

`x=6+9=15`