Question

4x-9y=9 -x+3y=6 Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.

Answer 1

the rewritten equation

`-4x+12y=24`

the equation in one variable:

`3y=33`

the solution for the system:

`y=11, x=27`

Explanation:

system of equations is:

`4x-9y=9 \\-x+3y=6`

If we multiply the second equation by 4, we can rewrite it like this:

`4(-x+3y=6)\\-4x+12y=24`

this last equation has the form
`ax+by=c`

so now we sum this equation to the unchanged equation:

`4x-9y=9\\-4x+12y=24\\--------------------\\0x +3y=33\\`

we get the equation with one variable
`3y=33`.

If you need to solve the whole system, we clear for y in the last equation:

`y=33/3\\y=11`

and using the first original equation we subtitute
`y` to find
`x`

`4x-9(11)=9\\4x-99=9\\4x=9+99\\4x=108\\x=108/4\\x=27`