66 Midterm 2: Version E

Find the solution set of the system graphically.

1. \(\left\{
   \begin{array}{rrrrr}
   x&-&y&=&-3 \\
   x&+&2y&=&3
   \end{array}\right.\)

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

2. \(\left\{
   \begin{array}{rrrrr}
   2x&-&5y&=&-2 \\
   3x&-&4y&=&4
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{rrrrr}
   4x&+&3y&=&-29 \\
   3x&+&2y&=&-21
   \end{array}\right.\)
4. \(\left\{
   \begin{array}{rrrrrrr}
   x&+&y&-&3z&=&0 \\
   &&2y&-&2z&=&-12 \\
   2x&-&3y&&&=&16
   \end{array}\right.\)

Reduce the following expressions in questions 5–7.

5. \(5 - 4 \left[ 2x - 2 (6x - 5)^0 - ( 7 - 2x )\right]\)
6. \(3ab^4(a - 5)(a + 5)\)
7. \((x^2 + 3x - 6)^2\)

Divide using long division.

8. \((3x^3 + 18 + 7x^2) \div (x + 3)\)

For problems 9–12, factor each expression completely.

9. \(x^2 + 4x - 21\)
10. \(4x^3 + 4x^2 - 9x - 9\)
11. \(8x^3 - 27y^3\)
12. \(x^4 - 624x^2 - 625\)

Solve the following word problems.

13. The sum of the ages of a boy and a girl is 20 years. Four years ago, the girl was two times the age of the boy. Find the present age of each child.
14. How many ml of a 16% sulfuric acid solution must be added to 20 ml of a 6% solution to create a 12% solution?
15. A 60 kg blend of cereals and raisins is sold for \(\$213.\) If the cereal sells for \(\$3.40\) per kg and the raisins sells for \(\$3.90\) per kg, how many kg of each grade were used?

Midterm 2: Version E Answer Key