# Thread: Alegebra Equations

1. ## Alegebra Equations

Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z

2. Originally Posted by Rimas
Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z
Hello,

you've got a system of 3 simultaneously equations:

$\displaystyle \begin {array}{l}3x+y\ \ =17 \\\ \ \ \ 5y+z=14 \\ 3x\ \ \ \ +5z=41 \end {array}$

I don't know which method you use to solve this system of equations. I solved the EQU1 for y and plugged this term into EQU2. I got:

3x + 5z = 41
-15x + z = -71

Multiply the 1rst equation by 5 and add:

26z = 134. Solve for z. Re-substitute this value and solve for x. Re-substitute the value of z in the EQU2 and solve for y.

You'll get:
$\displaystyle x=\frac{66}{13}\ \wedge \ y=\frac{23}{13}\ \wedge \ z=\frac{67}{13}$

The sum of these three numbers is 12

EB

3. Originally Posted by Rimas
Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z
Add the equations together:

(3x+y) + (5y+z) + (3x+5z) = 17 + 14 + 41

this simplifies to:

6x + 6y + 6z = 72,

divide by 6:

x + y + z = 12.

RonL