Midterm 2: Version E

Find the solution set of the system graphically.

1. [latex]\left\{ \begin{array}{rrrrr} x&-&y&=&-3 \\ x&+&2y&=&3 \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} 2x&-&5y&=&-2 \\ 3x&-&4y&=&4 \end{array}\right.[/latex]
3. [latex]\left\{ \begin{array}{rrrrr} 4x&+&3y&=&-29 \\ 3x&+&2y&=&-21 \end{array}\right.[/latex]
4. [latex]\left\{ \begin{array}{rrrrrrr} x&+&y&-&3z&=&0 \\ &&2y&-&2z&=&-12 \\ 2x&-&3y&&&=&16 \end{array}\right.[/latex]

Reduce the following expressions in questions 5–7.

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

Divide using long division.

8. [latex](3x^3 + 18 + 7x^2) \div (x + 3)[/latex]

For problems 9–12, factor each expression completely.

9. [latex]x^2 + 4x - 21[/latex]
10. [latex]4x^3 + 4x^2 - 9x - 9[/latex]
11. [latex]8x^3 - 27y^3[/latex]
12. [latex]x^4 - 624x^2 - 625[/latex]

Solve the following word problems.

13. The sum of the ages of a boy and a girl is 20 years. Four years ago, the girl was two times the age of the boy. Find the present age of each child.
14. How many ml of a 16% sulfuric acid solution must be added to 20 ml of a 6% solution to create a 12% solution?
15. A 60 kg blend of cereals and raisins is sold for [latex]\$213.[/latex] If the cereal sells for [latex]\$3.40[/latex] per kg and the raisins sells for [latex]\$3.90[/latex] per kg, how many kg of each grade were used?

Midterm 2: Version E Answer Key