# algabra questions, need help please!

• Nov 14th 2006, 07:42 AM
mathnoobie25
1. Solve the system of equation using the addition method
2x-3y=11
-3x=-5y-17

2. Kate and Ernie are at a dude ranch. Kate has been horseback riding for 0.5 hours on the trail at 6 miles per hour when ernie starts riding his horse on the trail. if ernie rides at 10 miles per hour, how long will it be before he catches up to kate.

3. using a graph, determine the solution of each system of inequalities.
2x+3y<6
4x-2y> or equal too 8.
• Nov 14th 2006, 08:19 AM
Soroban
Hello, mathnoobie25!

Here's the first one . . .

Quote:

1. Solve the system of equation using the addition method
. . 2x - 3y = 11
. . -3x = -5y - 17

We have: .$\displaystyle \begin{array}{cc}(1) \\(2)\end{array}\begin{array}{cc}2x - 3y\\\text{-}3x+ 5y\end{array} \begin{array}{cc}=\\=\end{array} \begin{array}{cc}11 \\\text{-}17\end{array}$

Multiply (1) by 5: .$\displaystyle 10x - 15y \:=\:55$
Multiply (2) by 3: .$\displaystyle \text{-}9x + 15y \:=\:\text{-}51$

Add and we get: .$\displaystyle \boxed{x\,=\,4}$

Substitute into (2): .$\displaystyle \text{-}3(4) + 5y \:=\:\text{-}17\quad\Rightarrow\quad 5y \,=\,\text{-}5\quad\Rightarrow\quad\boxed{ y \,=\,\text{-}1}$

Answer: .$\displaystyle \boxed{\begin{array}{cc}x\,=\,4\\y\,=\,\text{-}1\end{array}}$
• Nov 14th 2006, 08:43 AM
TriKri
Quote:

Originally Posted by mathnoobie25
1. Solve the system of equation using the addition method
2x-3y=11
-3x=-5y-17

2. Kate and Ernie are at a dude ranch. Kate has been horseback riding for 0.5 hours on the trail at 6 miles per hour when ernie starts riding his horse on the trail. if ernie rides at 10 miles per hour, how long will it be before he catches up to kate.

3. using a graph, determine the solution of each system of inequalities.
2x+3y<6
4x-2y> or equal too 8.

In the first system. multiply the first equation by 1.5 and add the two equations together and I'm sure you'll get it.
• Nov 14th 2006, 08:53 AM
TriKri
3.
2x+3y<6
4x-2y> or equal too 8

2x + 3y < 6
-4x - 6y > -12

(4x - 2y) + (-4x - 6y) > 8 - 12 = -4
-12y > -4
3y < 1
y < 1/3

y is unlimited in negative direction, but limited in positive direction, < 1/3.
x is unlimited in both directions.
Draw a graph and you'll se.
• Nov 15th 2006, 11:41 AM
TriKri
Or since for every value of x, there is values for y that fulfill system, you can make y depend on x.

$\displaystyle 2x + 3y < 6 \Rightarrow 3y < 6 - 2x \Rightarrow y < 2 - \frac{2}{3}x$

$\displaystyle 4x-2y \geq 8 \Rightarrow 2y \leq 4x - 8 \Rightarrow y \leq2x - 4$

So we now have two equations limiting y as a function of x (or something like that).