A lot of people find it easier to visualize what the least to greatest would look like. So imagine a number line that starts (in the middle) at 0. All numbers to the right get GREATER and GREATER. Going for 0 to 1 to 2.... and higher. Going to the left it gets LOWER and LOWER. So, -1 to -2 to -3 and onward. Basically what I'm trying to say is the farther you are to the left the smaller you are.
Another way you can think of it is you could remove the negative, and put them in order from least to greatest. Then when you add the negative back you would flip the order. So let's do that with our current problem: (Keep in mind that if you do this with sequences that are not all negative numbers you need to make the positive numbers negative. Or you can write out a number line and put all the numbers on it)
y = (152(32) -420(12))/(4(32) -12(12)) = -176/-16 = 11
The cost of the vegetarian lunch is 11.
_____
<em>Comment on Cramer's Rule</em>
For equations ...
ax +by =c
dx +ey = f
The solutions are ...
x = (bf -ey)/(bd -ea)
y = (cd -fa)/(bd -ea) . . . . note the denominators are the same expression
Once you memorize the pattern of products, this can be the simplest way to solve a pair of equations--especially if you only need one of the variable values.
