64 Midterm 2: Version C

Find the solution set of the system graphically.

1. \(\left\{
   \begin{array}{rrrrrrr}
   2x&-&y&-&2&=&0 \\
   2x&+&3y&+&6&=&0
   \end{array}\right.\)

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

2. \(\left\{
   \begin{array}{rrrrr}
   3x&-&4y&=&13 \\
   x&+&y&=&2
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{rrrrr}
   4x&-&3y&=&6 \\
   3y&+&4x&=&2
   \end{array}\right.\)
4. \(\left\{
   \begin{array}{rrrrrrr}
   x&+&y&+&z&=&6 \\
   &&2y&+&4z&=&10 \\
   -2x&&&+&z&=&-3 \\
   \end{array}\right.\)

Reduce the following expressions in questions 5–7.

5. \(36 + \{-2x - \left[6x - 3(5 - 2x)\right]\}^0 + 6x^3\)
6. \(6a^2b(a - 3)(a + 3)\)
7. \((x^2 + 3x + 5)^2\)

Divide using long division.

8. \((2x^4 + x^3 + 4x^2 - 4x - 5) \div (2x + 1)\)

For problems 9–12, factor each expression completely.

9. \(x^2 + 17x - 18\)
10. \(2a^2 - 4ab - 30b^2\)
11. \(8x^3 - y^3\)
12. \(16y^4 - x^4\)

Solve the following word problems.

13. The sum of a brother's and sister’s ages is 30. Ten years ago, the brother was four times his sister’s age. How old are they now?
14. Kyra gave her brother Mark a logic question to solve: If she has 18 coins in her pocket worth \(\$1.20\), and if the coins are only dimes and nickels, how many of each type of coin does she have?
15. Tanya needs to make 10 litres of a 25% alcohol solution for the University Green College Founders Social by mixing a 30% alcohol solution with a 5% alcohol solution. How many litres each of the 30% and the 5% alcohol solutions should be used?

Midterm 2: Version C Answer Key