Question

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

Answer 1

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

Answer 2

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