Answer:
the rewritten equation
[tex]-4x+12y=24[/tex]
the equation in one variable:
[tex]3y=33[/tex]
the solution for the system:
[tex]y=11, x=27[/tex]
Step-by-step explanation:
system of equations is:
[tex]4x-9y=9 \\-x+3y=6[/tex]
If we multiply the second equation by 4, we can rewrite it like this:
[tex]4(-x+3y=6)\\-4x+12y=24[/tex]
this last equation has the form [tex]ax+by=c[/tex]
so now we sum this equation to the unchanged equation:
[tex]4x-9y=9\\-4x+12y=24\\--------------------\\0x +3y=33\\[/tex]
we get the equation with one variable [tex]3y=33[/tex].
If you need to solve the whole system, we clear for y in the last equation:
[tex]y=33/3\\y=11[/tex]
and using the first original equation we subtitute [tex]y[/tex] to find [tex]x[/tex]
[tex]4x-9(11)=9\\4x-99=9\\4x=9+99\\4x=108\\x=108/4\\x=27[/tex]
