Find the solution set of the system graphically.

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

Reduce the following expressions in questions 5–7.

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

Divide using long division.

8. [latex](2x^3 - 7x^2 + 15) \div (x - 2)[/latex]

For problems 9–12, factor each expression completely.

9. [latex]2ab + 3ac - 4b - 6c[/latex]
10. [latex]a^2 - 2ab - 15b^2[/latex]
11. [latex]x^3 + x^2 - 9x - 9[/latex]
12. [latex]x^3 - 64y^3[/latex]

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 [latex]\$2.75[/latex], 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 [latex]\$191.25.[/latex] If grade A sells for [latex]\$3.95[/latex] per kg and grade B sells for [latex]\$3.70[/latex] per kg, how many kg of each grade were used?

Midterm 2: Version A Answer Key