Midterm 2: Version B

Find the solution set of the system graphically.

1. [latex]\left\{ \begin{array}{rrrrr} x&+&y&=&5 \\ 2x&-&y&=&1 \end{array}\right.[/latex]

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

2. [latex]\left\{ \begin{array}{rrrrrrr} 4x&+&3y&=&8&& \\ &&x&=&4y&+&2 \\ \end{array}\right.[/latex]
3. [latex]\left\{ \begin{array}{rrrrr} 5x&-&3y&=&2 \\ 3x&+&y&=&4 \end{array}\right.[/latex]
4. [latex]\left\{ \begin{array}{rrrrrrr} x&+&y&+&z&=&3 \\ x&&&-&2z&=&-7 \\ &&-2y&+&4z&=&20 \end{array}\right.[/latex]

Reduce the following expressions in questions 5–8.

5. [latex]5 - 3\left[4x - 2(6x - 5)^0 - (7 - 2x)\right][/latex]
6. [latex]3a^2(a + 3)^2[/latex]
7. [latex](x^2 + x + 5)(x^2 + x - 5)[/latex]
8. [latex]\left(\dfrac{x^{4n}x^{-6}}{x^{3n}}\right)^{-1}[/latex]

For problems 9–12, factor each expression completely.

9. [latex]14axy - 6az - 7xy + 3z[/latex]
10. [latex]a^2 + 2ab - 15b^2[/latex]
11. [latex]2x^3 + 8x^2 - x - 4[/latex]
12. [latex]27x^3 + 8y^3[/latex]

Solve the following word problems.

13. The sum of the ages of a father and his daughter is 38. Six years from now, the father will be four times as old as his daughter. Find the present age of each.
14. A 90 kg mixture of two different types of nuts costs [latex]\$370[/latex]. If type A costs [latex]\$3[/latex] per kg and type B costs [latex]\$5[/latex] per kg, how many kg of each type were used?
15. A student lab technician is combining a 10% sulfuric acid solution to 40 ml solution at 25% to dilute it to 15%. How much of the 10% solution does the student need to add?

Midterm 2: Version B Answer Key