In evaluating, we can simply plug in 4 and 2 for \(\displaystyle x\) and \(\displaystyle y\) respectively. We then get \(\displaystyle 16-16=0\).

The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives

\(\displaystyle \$0.20(x-10)+5\).

If we take the units and look at division, \(\displaystyle miles/(miles/hour)\) will yield hours as a unit. Therefore the answer is \(\displaystyle b/c\).

In general, \(\displaystyle distance=rate\times time\). 

The distance is the same going and coming; however, the head wind affects the rate.  The equation thus becomes \(\displaystyle (r-25)\times 5=(r+25)\times 4\).

Solving for \(\displaystyle r\) gives \(\displaystyle r=225\ mph\).

Pure water is 0% and pure solution 100%.  Let \(\displaystyle x\) = water to be added.

\(\displaystyle V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}\)  in general where \(\displaystyle V\) is the volume and \(\displaystyle P\) is the percent.

So the equation to solve becomes \(\displaystyle x(0)+2(0.90)= (x+2)(0.50)\)

and \(\displaystyle x=1.6\ L\)

This problem is a good example of the substitution method of solving a system of equations.  We start by rewritting the first equation in terms of \(\displaystyle x\) to get \(\displaystyle x=14-2y\) and then substutite the \(\displaystyle x\) into the second equation to get

\(\displaystyle 2(14-2y)+y=13\). 

Solving this equation gives \(\displaystyle y=5\) and substituting this value into one of the original equations gives \(\displaystyle x=4\), thus the correct answer is \(\displaystyle (4,5)\).

Let \(\displaystyle x\) = # of color pencil boxes and \(\displaystyle x+1\) = # of sketch pads purchased.

So the equation to solve becomes \(\displaystyle 1.25x+2.25(x+1)=9.25\). 

Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.

This question deals with absolute value equations which will normally gives you two solutions.

You need to solve two sets of equations for absolute value problems:

\(\displaystyle 2x-3 = x+5\)

and

\(\displaystyle 2x-3=-\left ( x+5 \right )\)

Let \(\displaystyle y\) = money earned and \(\displaystyle x\) = number of cars sold

So \(\displaystyle y = 500x + 1000\)

\(\displaystyle 7500 = 500x + 1000\) and solving shows that he needs to sell 13 cars to make $7,500.

Let pure water = 0 % and pure acid = 100%

The general equation to use is:

\(\displaystyle V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}\)  where \(\displaystyle V\)is the volume and \(\displaystyle P\)is the percent solution.

So the equation to solve becomes \(\displaystyle x(0) + 2(.80) = (x + 2)(.20)\) and \(\displaystyle x = 6\) gallons of pure water needs to be added to get a 20% acid solution.