Find the solution set of the system graphically.

1. $\{\begin{array}{rrrrr}x& +& y& =& 5\\ 2x& -& y& =& 1\end{array}$

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

2. $\{\begin{array}{rrrrrrr}4x& +& 3y& =& 8& & \\ & & x& =& 4y& +& 2\end{array}$
3. $\{\begin{array}{rrrrr}5x& -& 3y& =& 2\\ 3x& +& y& =& 4\end{array}$
4. $\{\begin{array}{rrrrrrr}x& +& y& +& z& =& 3\\ x& & & -& 2z& =& -7\\ & & -2y& +& 4z& =& 20\end{array}$

Reduce the following expressions in questions 5–8.

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

For problems 9–12, factor each expression completely.

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

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 $\mathrm{\$}370$. If type A costs $\mathrm{\$}3$ per kg and type B costs $\mathrm{\$}5$ 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