Question

Solve the system using any algebraic method. Show all your steps.

Answer 1

$First\ system\ of\ equations:\\ \left \{ {{2x-5y=3} \atop {-4x+10y=-6}} \right. second\ equation\ divide\ by\ 2\\ \left \{ {{2x-5y=3} \atop {-2x+5y=-3}}\right.\\+--------\\0=0\\There\ are\ infinitely\ many\ solutions\\\\Second\ system\ of\ equations:\\ \left \{ {{8x+3y=10} \atop {-6x+y=-12}} \right.second\ equation\ multiply\ by\ -3\\ \left \{ {{8x+3y=10} \atop {18x-3y=36}} \right\\+--------\\26x=46\\x= \frac{46}{26}= \frac{23}{13} \\-6x+y=-12\\y=-12+6x\\y=-12+6* \frac{23}{13}\\y=-12+\frac{138}{13}$
$y=-12+10 \frac{8}{13} \\y=-1 \frac{5}{13}$