1. ## Elimination and substitution

I have this problem: y=1x and y=.5x+4
I got (2,4) and was wondering if you guys can show me the steps for both elimination and substitution. Also how would I graph this? just put one dot on the graph?

2. Originally Posted by Jubbly
I have this problem: y=1x and y=.5x+4
I got (2,4) and was wondering if you guys can show me the steps for both elimination and substitution. Also how would I graph this? just put one dot on the graph?
How did you get $\displaystyle (2,4)?$ If you try checking your work by substituting, you get

$\displaystyle x=2\Rightarrow y=2$

for the first, and

$\displaystyle x=2\Rightarrow y=5$

for the second. Your point is not on either of the curves, so it certainly could not be in the solution set.

3. Well, I did 1x=.5x+4
I subtracted .5x from both sides making 1x and .5x
now its .5x=4
divided .5x into 4 and got 2
so x=2?

Can you show me a step by step of how your doing it and how your substituting?

4. Originally Posted by Jubbly
divided .5x into 4 and got 2
4 divided by 0.5 is 8, not 2:

$\displaystyle \frac4{1/2}=4\cdot\frac21=4\cdot2=8\text.$

The correct solution is $\displaystyle (8,\,8)\text.$

If you don't mind can you show me the elimination and substitution equation you used for this. Thanks!

6. Certainly. We have

$\displaystyle \left\{\begin{array}{rcl} y&=&x\\ y&=&\frac12x+4 \end{array}\right.$

Substitution:

Substituting $\displaystyle x=y$ into the second equation produces

$\displaystyle y=\frac12y+4,$

and solving for $\displaystyle y$ gives

$\displaystyle \frac12y=4\Rightarrow y=8.$

Back-substituting, we get $\displaystyle x=8.$

Elimination:

Let's first rearrange the equations a little,

$\displaystyle \left\{\begin{array}{rcl} y-x&=&0\\ 2y-x&=&8 \end{array}\right..$

Subtract the first equation from the second,

$\displaystyle \left\{\begin{array}{rcl} y-x&=&0\\ y&=&8 \end{array}\right.$

and subtract the second equation from the first:

$\displaystyle \left\{\begin{array}{rcl} -x&=&-8\\ y&=&8 \end{array}\right.\Rightarrow\left\{\begin{array}{ rcl} x&=&8\\ y&=&8 \end{array}\right.$