63 Midterm 2: Version B

Find the solution set of the system graphically.

1. \(\left\{
   \begin{array}{rrrrr}
   x&+&y&=&5 \\
   2x&-&y&=&1
   \end{array}\right.\)

For problems 2–4, find the solution set of each system by any convenient method.

2. \(\left\{
   \begin{array}{rrrrrrr}
   4x&+&3y&=&8&& \\
   &&x&=&4y&+&2 \\
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{rrrrr}
   5x&-&3y&=&2 \\
   3x&+&y&=&4
   \end{array}\right.\)
4. \(\left\{
   \begin{array}{rrrrrrr}
   x&+&y&+&z&=&3 \\
   x&&&-&2z&=&-7 \\
   &&-2y&+&4z&=&20
   \end{array}\right.\)

Reduce the following expressions in questions 5–8.

5. \(5 - 3\left[4x - 2(6x - 5)^0 - (7 - 2x)\right]\)
6. \(3a^2(a + 3)^2\)
7. \((x^2 + x  + 5)(x^2 + x  - 5)\)
8. \(\left(\dfrac{x^{4n}x^{-6}}{x^{3n}}\right)^{-1}\)

For problems 9–12, factor each expression completely.

9. \(14axy - 6az - 7xy + 3z\)
10. \(a^2 + 2ab - 15b^2\)
11. \(2x^3 + 8x^2 - x - 4\)
12. \(27x^3 + 8y^3\)

Solve the following word problems.

13. The sum of the ages of a father and his daughter is 38. Six years from now, the father will be four times as old as his daughter. Find the present age of each.
14. A 90 kg mixture of two different types of nuts costs \(\$370\). If type A costs \(\$3\) per kg and type B costs \(\$5\) per kg, how many kg of each type were used?
15. A student lab technician is combining a 10% sulfuric acid solution to 40 ml solution at 25% to dilute it to 15%.  How much of the 10% solution does the student need to add?

Midterm 2: Version B Answer Key