65 Midterm 2: Version D

Find the solution set of the system graphically.

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

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

2. \(\left\{
   \begin{array}{rrrrr}
   3x&-&2y&=&0 \\
   2x&+&5y&=&0
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{rrrrr}
   2x&-&3y&=&8 \\
   3y&-&2x&=&4
   \end{array}\right.\)
4. \(\left\{
   \begin{array}{rrrrrrr}
   2x&+&y&-&3z&=&-7 \\
   &&-2y&+&3z&=&9 \\
   3x&&&+&z&=&6
   \end{array}\right.\)

Reduce the following expressions in questions 5–7.

5. \(36 - \{-2x - \left[6x - 3(5 - 2x)\right]\}^0 + 3x^2\)
6. \(3a^2(a - 2)^2\)
7. \((x^2 + 2x - 4)^2\)

Divide using long division.

8. \((x^4 +  4x^3 +  4x^2 + 10x + 20) \div (x + 2)\)

For problems 9–12, factor each expression completely.

9. \(x^2 + 3x - 18\)
10. \(3x^2 + 25xy + 8y^2\)
11. \(125x^3 -  y^3\)
12. \(81y^4 - 16x^4\)

Solve the following word problems.

13. The sum of the ages of a boy and a girl is 18 years. Four years ago, the girl was four times the age of the boy. Find the present age of each child.
14. A purse contains \(\$3.50\) made up of dimes and quarters. If there are 20 coins in all, how many dimes and how many quarters were there?
15. A 60 kg blend of two different grades of tea is sold for \(\$218.50.\) If grade A sells for \(\$3.80\) per kg and grade B sells for \(\$3.55\) per kg, how many kg of each grade were used?

Midterm 2: Version D Answer Key