Question

SOLVE BY ELIMINATION - SHOW YOUR WORK! I need to know which method can be used for this specific problem. Thanks!

Answer 1

elimination, namely we'll eliminate a variable.

let's notice say 4y and 3y in the y-column, now, if we multiply 3*4y = 12y, and if we multiply 4*-3y = -12y, and those 12y-12y cancel each other out, so we'll do that.

$\bf \begin{cases} 5x+4y=12\\ 3x-3y=18 \end{cases} ~\hfill \begin{array}{lllllll} 5x+4y=12&&\times 3\implies &15x+12y=36\\ 3x-3y=18&&\times 4\implies &12x-12y=72\\ \cline{4-4}\\ &&&27x+0y=108 \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 27x=108\implies x=\cfrac{108}{27}\implies \blacktriangleright x=4 \blacktriangleleft$

$\bf \stackrel{\textit{substituting the \boxed{x} in the 2nd equation}}{3(4)-3y=18\implies 12-3y=18}\implies -3y=6 \\\\\\ y=\cfrac{6}{-3}\implies \blacktriangleright y=-2 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (4,-2)~\hfill$