What’s the fastest way to do test 5 #18 in the no calculator section?

Because this is a no calculator question, it is worth your while to take a second to strategize before you dive in. In this case, a couple seconds of thinking will tell you two things:

  1. Those fractions will be easy to cancel out if you multiply by 2.
  2. You’re only asked to solve for x, so substitute accordingly.

First, cancel out the fraction:

    \begin{align*}\dfrac{1}{2}(2x+y)&=\dfrac{21}{2}\\2\left(\dfrac{1}{2}(2x+y)\right)&=2\left(\dfrac{21}{2}\right)\\2x+y&=21\end{align*}

Now take the second equation, y=2x, and substitute:

    \begin{align*}2x+y&=21\\2x+2x&=21\\4x&=21\\x&=\dfrac{21}{4}\end{align*}

You can grid in that fraction or its decimal equivalent: 5.25.