# 9 ?'s that i really need help on!!!

• Jul 31st 2006, 08:58 AM
Lane
9 ?'s that i really need help on!!!
questions are on attachment!
• Jul 31st 2006, 09:12 AM
galactus
#1:

Let x=amount invested at 10%.

Then 3500-x is the amount invested at 15%.

The difference between the two interest rates is $85.$\displaystyle .15(3500-x)-.10x=85$Also, how about showing some of your attempts instead of just posting a littany of problems. • Jul 31st 2006, 12:27 PM Soroban Hello, Lane! Here are a few more . . . Quote: Solve: .$\displaystyle \begin{array}{cc}3x - 4y \,= \,7 \\ x + 2y \,=\,9\end{array}$With no method specified, I'll use Elimination. We have: .$\displaystyle \begin{array}{cc}3x - 4y \:= \:7 \\ x + 2y \:=\:9\end{array}\;\begin{array}{cc}(1)\\(2)\end{a rray}$Multiply (2) by 2: .$\displaystyle 2x + 4y \:=\:18$. . . . . . Add (1): .$\displaystyle 3x - 4y \:=\:7$And we have: .$\displaystyle 5x\,=\,25\quad\Rightarrow\quad \boxed{x = 5}$Substitute into (2): .$\displaystyle 5 + 2y\:=\:9\quad\Rightarrow\quad 2y \,=\,4\qiad\Rightarrow\quad \boxed{y = 2}$Quote: Solve with Cramer's Rule: .$\displaystyle \begin{array}{cc}6x - 4y \:=\:6 \\ 3x \:= \:2y - 5\end{array}$We have: .$\displaystyle \begin{array}{cc}6x-4y\:=\:7\\3x-2y\:=\:\text{-}5\end{array}\displaystyle D\:=\:\begin{vmatrix}6 & \text{-}4 \\ 3 & \text{-}2\end{vmatrix} \;= \;(6)(\text{-}2) - (\text{-}4)(3) \;= \;-12 + 12 \;= \;0$. . . No solution! Quote: 6. Solve: .$\displaystyle \begin{array}{cc}xy\:=\:10 \\ x^2 + 4y^2\:=\:36\end{array}\;\begin{array}{cc}(1)\\(2) \end{array}$Another trick question! From (1), we have: .$\displaystyle y = \frac{10}{x}$Substitute into (2): .$\displaystyle x^2 + 4\left(\frac{10}{x}\right)^2\;=\;36 \quad\Rightarrow\quad x^2 + \frac{400}{x^2}\:=\:36$Multiply by$\displaystyle x^2:\;\;x^4 + 400 \:=\:36x^2\quad\Rightarrow\quad x^4 - 36x^2 + 400 \:= \:0$Quadratic Formula: .$\displaystyle x^2\:=\:\frac{-(\text{-}36) \pm \sqrt{(\text{-}36)^2 - 4(1)(400)}}{2(1)}$. . .$\displaystyle x^2\;=\;\frac{36 \pm\sqrt{-304}}{2}\$ . . . No real root

Therefore, the system has no real solution.