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

Answer:

the rewritten equation

$-4x+12y=24$

the equation in one variable:

$3y=33$

the solution for the system:

$y=11, x=27$

Step-by-step 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 $x$

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