1. ## algabra questions, need help please!

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.

2. Hello, mathnoobie25!

Here's the first one . . .

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

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

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

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

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

Answer: . $\boxed{\begin{array}{cc}x\,=\,4\\y\,=\,\text{-}1\end{array}}$

3. 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.

4. 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.

5. Or since for every value of x, there is values for y that fulfill system, you can make y depend on x.

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

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

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