# SOLUTION: solve the system of equations. 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 im not sure how to do this. i would greatly appreciate any help. thank you

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: solve the system of equations. 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 im not sure how to do this. i would greatly appreciate any help. thank you      Log On

 Algebra: Linear Algebra (NOT Linear Equations) Solvers Lessons Answers archive Quiz In Depth

 Question 282372: solve the system of equations. 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 im not sure how to do this. i would greatly appreciate any help. thank youAnswer by Alan3354(31538)   (Show Source): You can put this solution on YOUR website!solve the system of equations. 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 ----------------- There's more than one way, but I'll use substitution since there's no x term in the 2nd eqn. -------------- 2y+z=3 --> z = 3-2y Sub for z in the other 2 eqns 3x + 4y + (3-2y) = 7 -5x + 3y +8(3-2y) = -31 ---------------- 3x + 2y = 4 -5x -13y = -55 Now it's 2 eqn in 2 variables. Multiply the 1st by 5 and the 2nd by 3 15x + 10y = 20 -15x -39y = -165 ---------------- Add -29y = -145 y = 5 ------- Sub for y in 3x + 2y = 4 --> x = -2 ------------- 2y+z=3 --> z = -7 ------------- If you're gonna do a lot of these, use Excel and determinants.