Find the solution set of the system graphically.

1. [latex]\left\{ \begin{array}{rrrrrrr} x&-&2y&+&6&=&0 \\ x&+&y&-&6&=&0 \end{array}\right.[/latex]

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

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

Reduce the following expressions in questions 5–7.

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

Divide using long division.

8. [latex](x^4 +  4x^3 +  4x^2 + 10x + 20) \div (x + 2)[/latex]

For problems 9–12, factor each expression completely.

9. [latex]x^2 + 3x - 18[/latex]
10. [latex]3x^2 + 25xy + 8y^2[/latex]
11. [latex]125x^3 -  y^3[/latex]
12. [latex]81y^4 - 16x^4[/latex]

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 [latex]\$3.50[/latex] 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 [latex]\$218.50.[/latex] If grade A sells for [latex]\$3.80[/latex] per kg and grade B sells for [latex]\$3.55[/latex] per kg, how many kg of each grade were used?

Midterm 2: Version D Answer Key