Question 1193249

1.Solve the system of equations. 
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10
<pre>There she goes again!!
For your sanity you need to IGNORE that woman's attempt to solve this system.

{{{system(matrix(3,6, x - 2y + 3z, "=", 7, "----", eq, "(i)", 2x + y + z, "=", 4, "----", eq, "(ii)", - 3x + 2y - 2z, "=", - 10, "----", eq, "(iii)"))}}}
   4x + 2y + 2z = 8 ------ Multiplying eq (ii) by 2 ------ eq (iv)
        5x + 5z = 15 ----- Adding eqs (iv) & (i) 
       5(x + z) = 5(3)_____x + z = 3 ------ eq (v)
       - 2x + z = - 3 -----Adding eqs (i) & (iii) ------ eq (vi)
             3x = 6 ------ Subtracting eq (vi) from eq (v)
             {{{highlight_green(matrix(1,5, x, "=", 6/3, "=", 2))}}}

          2 + z = 3 ------- Substituting 2 for x in eq (v)
             <font color = blue><font size = 4><b>z = 3 - 2 = 1</font></font></b>
   
   2(2) + y + 1 = 4 ------- Substituting 2 for x and 1 for z in eq (ii)
      4 + y + 1 = 4
          y + 5 = 4
             <font color = blue><font size = 4><b>y = 4 - 5 = - 1</font></font></b>
 
   <font color = red><font size = 4><b>You can do the CHECKS!!</font></font></b>
</pre>