Question

a test is worth 80 points.multiple choice questions are worth 2 points,and short-answer questions are worth 4 points.if the test has 25 questions,how many multiple-choice questions are there?

Answer 1

Let $x$ be the number of multiple choice questions and $y$ the number of short-answer questions.

Now,

$\begin{cases}x+y=25\\2x+4y=80\end{cases}$

Since you only care about finding $y$, you can substitute the first equation into the second to eliminate $x$. You have

$x+y=25\implies x=25-y$

and substituting into the other equation,

$2(25-y)+4y=80$
$50-2y+4y=80$
$2y=30$
$y=15$