document.write( "Question 827544: Solve the system using substitution.\r
\n" ); document.write( "\n" ); document.write( "x + 6z = -45
\n" ); document.write( "5x + 3y - 2z = -33
\n" ); document.write( "y + 4z = -24\r
\n" ); document.write( "\n" ); document.write( "I think i keep messing up the first step because when im finished i get
\n" ); document.write( "x=-9, y=8, z=-6, but it doesnt work when pluging it back in \n" ); document.write( "
Algebra.Com's Answer #498743 by TimothyLamb(4379)\"\" \"About 
You can put this solution on YOUR website!
---
\n" ); document.write( "x + 6z = -45
\n" ); document.write( "5x + 3y - 2z = -33
\n" ); document.write( "y + 4z = -24
\n" ); document.write( "---
\n" ); document.write( "copy and paste the above linear system in standard form into this matrix-method solver:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php
\n" ); document.write( "---
\n" ); document.write( "solution by matrix-method:
\n" ); document.write( "x = -9
\n" ); document.write( "y = 0
\n" ); document.write( "z = -6
\n" ); document.write( "---
\n" ); document.write( "system matrix
\n" ); document.write( "1 0 6
\n" ); document.write( "5 3 -2
\n" ); document.write( "0 1 4
\n" ); document.write( "---
\n" ); document.write( "inverse of system matrix
\n" ); document.write( "0.31818182 0.13636364 -0.40909091
\n" ); document.write( "-0.45454545 0.090909091 0.72727273
\n" ); document.write( "0.11363636 -0.022727273 0.068181818
\n" ); document.write( "---
\n" ); document.write( "determinant of system matrix = 44
\n" ); document.write( "---
\n" ); document.write( "now by substitution:
\n" ); document.write( "---
\n" ); document.write( "x + 6z = -45
\n" ); document.write( "x = -6z - 45
\n" ); document.write( "---
\n" ); document.write( "5x + 3y - 2z = -33
\n" ); document.write( "5(-6z - 45) + 3y - 2z = -33
\n" ); document.write( "-30z - 225 + 3y - 2z = -33
\n" ); document.write( "---
\n" ); document.write( "3y - 32z = 192
\n" ); document.write( "---
\n" ); document.write( "y + 4z = -24
\n" ); document.write( "y = -4z - 24
\n" ); document.write( "---
\n" ); document.write( "3y - 32z = 192
\n" ); document.write( "3(-4z - 24) - 32z = 192
\n" ); document.write( "-12z - 72 - 32z = 192
\n" ); document.write( "-44z = 264
\n" ); document.write( "z = -264/44
\n" ); document.write( "---
\n" ); document.write( "z = -6
\n" ); document.write( "---
\n" ); document.write( "y = -4z - 24
\n" ); document.write( "y = -4(-6) - 24
\n" ); document.write( "---
\n" ); document.write( "y = 0
\n" ); document.write( "---
\n" ); document.write( "x = -6z - 45
\n" ); document.write( "x = -6(-6) - 45
\n" ); document.write( "---
\n" ); document.write( "x = -9
\n" ); document.write( "---
\n" ); document.write( "---
\n" ); document.write( "solution by substitution-method:
\n" ); document.write( "x = -9
\n" ); document.write( "y = 0
\n" ); document.write( "z = -6
\n" ); document.write( "---
\n" ); document.write( "the two methods agree.
\n" ); document.write( "---
\n" ); document.write( "Solve and graph linear equations:
\n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve quadratic equations, quadratic formula:
\n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve systems of linear equations up to 6-equations 6-variables:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php \n" ); document.write( "
\n" );