Find the solution set of the system graphically.

1. [latex]\left\{ \begin{array}{rrrrrrr} 2x&-&y&-&2&=&0 \\ 2x&+&3y&+&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&-&4y&=&13 \\ x&+&y&=&2 \end{array}\right.[/latex]
3. [latex]\left\{ \begin{array}{rrrrr} 4x&-&3y&=&6 \\ 3y&+&4x&=&2 \end{array}\right.[/latex]
4. [latex]\left\{ \begin{array}{rrrrrrr} x&+&y&+&z&=&6 \\ &&2y&+&4z&=&10 \\ -2x&&&+&z&=&-3 \\ \end{array}\right.[/latex]

Reduce the following expressions in questions 5–7.

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

Divide using long division.

8. [latex](2x^4 + x^3 + 4x^2 - 4x - 5) \div (2x + 1)[/latex]

For problems 9–12, factor each expression completely.

9. [latex]x^2 + 17x - 18[/latex]
10. [latex]2a^2 - 4ab - 30b^2[/latex]
11. [latex]8x^3 - y^3[/latex]
12. [latex]16y^4 - x^4[/latex]

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 [latex]\$1.20[/latex], 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