<s>[INST] How to calculate per unit cost? I need help understanding this math problem from my TEAS Mometrix Practice exam. It gives an explanation but I still don't understand. The question is:
Mandy can buy $4$ containers of yogurt and $3$ boxes of crackers for $\$9.55$. She can buy $2$ containers of yogurt and $2$ boxes of crackers for $\$5.90$. How much does one box of crackers cost?
The answer is $ \$2.25$.
I understand that I have to set up the problem like this:
\begin{align}
4x+3y &= 9.55 \\
2x+2y &= 5.90
\end{align}
but the explanation says that I have to multiply the bottom equation by $-2$; therefore, it becomes $-4x+ -4y= -11.80$
and then  I have to add the equations 
\begin{align}
4x+3y   &= 9.55\\
-4x+-4y &= -11.80
\end{align}
by top to bottom getting  either $\pm 2.25$
Can you explain why this is the answer? And also why does one have multiply by -2?
 [/INST] There are several ways to solve this or similar problems we have 
$$4 \cdot x + 3 \cdot y = 9.55 \\
2 \cdot x  + 2 \cdot y = 5.90$$
One approch as given in your answer is to multiply the second equation by 2 or -2 you then have $4 \cdot x$ in both equations so can cancel for $x$ by adding the two equations or subtracting the equations as appropriate.  The reason this works is that by multiplying all terms by the same number you have created another true statement.
This is not the only approach however,  Another approach would be for example to solve one equation for say $y$ then substituting it in the other.
$$2 \cdot x + 2 \cdot y = 5.90 \Rightarrow y = \frac{5.90 - 2 \cdot x}{2}$$
Putting that in the other equation we have
$$4 \cdot x + 3 \cdot y = 4 \cdot x + 3 \cdot \frac{5.90 - 2 \cdot x}{2} = 4 \cdot x + 8.85 - 3 \cdot x= 9.55 \Rightarrow x = 9.55 - 8.85 = 0.7$$
Putting this back in the other equation
$$ 2 \cdot x + 2 \cdot y = 2 \cdot 0.7 +2 \cdot y = 5.90 \Rightarrow y = \frac{5.9 - 1.4}{2} = 2.25$$
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