62 Midterm 2: Version A

Find the solution set of the system graphically.

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

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

2. \(\left\{
   \begin{array}{rrrrr}
   4x&-&3y&=&13 \\
   5x&-&2y&=&4
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{rrrrr}
   x&-&2y&=&-5 \\
   2x&+&y&=&5
   \end{array}\right.\)
4. \(\left\{
   \begin{array}{rrrrrrr}
   x&+&y&+&2z&=&0 \\
   2x&&&+&z&=&1 \\
   &&3y&+&4z&=&0
   \end{array}\right.\)

Reduce the following expressions in questions 5–7.

5. \(28 - \{5x - \left[6x - 3(5 - 2x)\right]^0 \} + 5x^2\)
6. \(4a^2 (a - 3)^2\)
7. \((x^2 + 2x + 3)^2\)

Divide using long division.

8. \((2x^3 - 7x^2 + 15) \div (x - 2)\)

For problems 9–12, factor each expression completely.

9. \(2ab + 3ac - 4b - 6c\)
10. \(a^2 - 2ab - 15b^2\)
11. \(x^3 + x^2 - 9x - 9\)
12. \(x^3 - 64y^3\)

Solve the following word problems.

13. The sum of a brother's and sister’s ages is 35. Ten years ago, the brother was twice his sister’s age. How old are they now?
14. Kyra gave her brother Mark a logic question to solve: If she has 20 coins in her pocket worth \(\$2.75\), and if the coins are only dimes and quarters, how many of each kind of coin does she have?
15. A 50 kg blend of two different grades of tea is sold for \(\$191.25.\) If grade A sells for \(\$3.95\) per kg and grade B sells for \(\$3.70\) per kg, how many kg of each grade were used?

Midterm 2: Version A Answer Key