Let chairs be
![c](https://tex.z-dn.net/?f=c)
and table be
![t](https://tex.z-dn.net/?f=t)
We form two equations from the information given so we can solve simultaneously
Eq 1 ⇒
![5c+3t=35](https://tex.z-dn.net/?f=5c%2B3t%3D35)
Eq 2 ⇒
We can either use the method of elimination or substitution. We will use the elimination method for this one
Let us eliminate the term
![c](https://tex.z-dn.net/?f=c)
. We need to make the two constants the same. We have
![5c](https://tex.z-dn.net/?f=5c)
and
![7c](https://tex.z-dn.net/?f=7c)
and we can make them both as
![35c](https://tex.z-dn.net/?f=35c)
.
We will multiply each term in Eq 1 by 7 to obtain
![35c+21t=245](https://tex.z-dn.net/?f=35c%2B21t%3D245)
We will multiply each term in Eq 2 by 5 to obtain
![35c+45t=455](https://tex.z-dn.net/?f=35c%2B45t%3D455)
Now we subtract Eq 2 from Eq 1 to obtain
![(35c-35c)+(21t-45t)=(245-455)](https://tex.z-dn.net/?f=%2835c-35c%29%2B%2821t-45t%29%3D%28245-455%29)
![-24t=-210](https://tex.z-dn.net/?f=-24t%3D-210)
![t= \frac{210}{24}=8.75](https://tex.z-dn.net/?f=t%3D%20%5Cfrac%7B210%7D%7B24%7D%3D8.75%20)
So the price of one table is $8.75
Substitute 8.75 into either Eq 1 or Eq 2 to obtain the price for one chair. Let's use Eq 1
![5c+3(8.75)=35](https://tex.z-dn.net/?f=5c%2B3%288.75%29%3D35)
![5c+26.25=35](https://tex.z-dn.net/?f=5c%2B26.25%3D35)
![5c=35-26.25](https://tex.z-dn.net/?f=5c%3D35-26.25)
![5c=8.75](https://tex.z-dn.net/?f=5c%3D8.75)
![c=1.75](https://tex.z-dn.net/?f=c%3D1.75)
So the price of one chair is $1.75