5x + 6y = 18 and 18x - 15y = 36

5x+6y=18

5x=18-6y

x = (18-6y) / 5

Use that in the other equation

18 (18-6y) / 5 - 15y = 36

64.8-21.6y - 15y = 36

28.8=36.6y

.7868=y

Now put that number in for y on the first equation

5x+6 (.78) = 18

5x + 4.68 = 18

5x = 13.32

x = 2.66

and y =.78

Solution : {x, y, z} = {-3,-2,-1} System of Linear Equations entered : [1] x + 6y + 3z = - 18 [2] - x + 6y - 3z = - 6 [3] 5x - 6y + 3z = - 6 Solve by Substitution:

/ / Solve equation [1] for the variable x

[1] x = - 6y - 3z - 18

/ / Plug this in for variable x in equation [2]

[2] - (-6y-3z-18) + 6y - 3z = - 6 [2] 12y = - 24

/ / Plug this in for variable x in equation [3]

[3] 5• (-6y-3z-18) - 6y + 3z = - 6 [3] - 36y - 12z = 84

/ / Solve equation [2] for the variable y

[2] 12y = - 24 [2] y = - 2

/ / Plug this in for variable y in equation [3]

[3] - 36• (-2) - 12z = 84 [3] - 12z = 12

/ / Solve equation [3] for the variable z

[3] 12z = - 12 [3] z = - 1

/ / By now we know this much:

x = - 6y-3z-18 y = - 2 z = - 1

/ / Use the y and z values to solve for x

x = - 6 (-2) - 3 (-1) - 18 = - 3

Solution : {x, y, z} = {-3,-2,-1} Processing ends successfully