text: systems of equations in three variables? i know this might be a lot of work if you're doing it on paper, but if you can just give me the answers to:  2x-y+2x=15 -x+y+z=3 3x-y+2z=18  a+b=2 -b+c=3 a+2c=10  2x+3y+4z=2 5x-2y+3z=0 x-5y-2z=-4  2x-5y+z=5 3x+2y-z=17 4x-3y+2z=17  x+y+z=6 z=x+y x=z+1 2x - y + 2z = 15- - - - - -equation 1 -x + y + z = 3- - - - - - - equation 2 3x - y + 2z = 18- - -- -  - equation 3 - - - - - - - - - - - -  elimination of y equation 1 and equation 2  2x - y + 2z = 15 -x + y + z = 3 - - - - - - - - - - - x + 3z = 18 . . equation 4  - - - - - - - - - - - - - - multiply equation 3 by - 1  3x - y + 2z = 18 - 1(3x) - 1(-y) + (- 1)(2z) = - 1(18) -3x + y - 2z = - 18. . .new equation 3  -- - - - - - - - - - - - - - -  elimination of y and z equation 1 and new equation 3  2x - y + 2z = 15 -3x + y - 2z = - 18 - - - - - - - - - - - -  - x = - 3  -1x = -3/-1  x = 3  the answer is x = 3  insert the x value into equation 4  - - - - - - - - - - - - - -  solving for z  x + 3z = 18  3 + 3z = 18  3 + 3x - 3 = 18 - 3  3z = 15  3z/3 = 15/3  z = 5  the answer is z = 5  insert the z value into equation 1  - - - - - - - - - - - - - - - - - - - - - -  solving for y equation 1  2x - y + 2z = 15  2(3) -y  + 2(5) = 15  6 - y + 10 = 15  16 - y = 15  16 - y - 16 = 15 - 16  - y = - 1  - 1y = - 1  -1y/-1 = - 1/- 1  y = 1  the answer is y = 1  insert the y value into equation 1  - - - - - - - - - - - - - - - - - - - - - -  check for equation 1  2x - y + 2z = 15  2(3) - 1 + 2(5) = 15  6 - 1 + 10 = 15  5 + 10 = 15  15 = 15  - - - - - - - - - - - - - - - -  check for equation 2  - x + y + z = 3  - 3 + 1 + 5 = 3  -2 + 5 = 3  3 = 3  - - - - - - - - - - - - -   check for equation 3  3x - y + 2z = 18  3(3) - 1 + 2(5) = 18  9 - 1 + 10  8 + 10 = 18  18 = 18  - - - - - - - - - - - - - - -  the solution set is { 3, 1, 5 }  - - - - - - - -s-