Question

Four glasses of milk and 3 snack bars have a total of 93 carbs, and 2 glasses of milk and 4 snack bars have a total of 74 carbs. Determine how many carbs are in one glass of milk and in one snack bar

Answer 1

Ok... we'll do the same here, elimination

g = carbs in one glass of milk
b = carbs in a snack bar

$\bf \begin{array}{llcll} 4g+3b=93&\implies &4g+3b=93\\ 2g+4b=74&\boxed{-2}\implies &-4g-8b=-148\\ &&----------\\ &&0-5b=-55 \end{array} \\\\\\ -5b=-55\implies b=\cfrac{-55}{-5}\implies \boxed{b=11}\\\\ -------------------------------\\\\ \textit{let's plug that in either, hmm the second equation}\\\\ 2g+4(11)=74\implies 2g+44=74\implies 2g=74-44 \\\\\\ 2g=30\implies g=\cfrac{30}{2}\implies \boxed{g=15}$

in this, we can simply multiply by -2 at the bottom to get a -4g, and thus "eliminate" the g-variable