Solve the given set of three equations to get the value of the unknowns:
x + 2z = 3
x + 2y + 3z = 5
3x - 5z = -13

Question

Solve the given set of three equations to get the value of the unknowns:  
x + 2z = 3   
x + 2y + 3z = 5   
3x - 5z = -13

Accepted Answer

Given the system:
1) x + 2z = 3
2) x + 2y + 3z = 5
3) 3x - 5z = -13

Step 1: From equation (1), express x in terms of z:
   x = 3 - 2z

Step 2: Substitute x into equation (3):
   3(3 - 2z) - 5z = -13
   9 - 6z - 5z = -13
   9 - 11z = -13
   -11z = -22
   z = 2

Step 3: Substitute z = 2 back into x = 3 - 2z:
   x = 3 - 2*2 = 3 - 4 = -1

Step 4: Substitute x and z into equation (2) to find y:
   -1 + 2y + 3*2 = 5
   -1 + 2y + 6 = 5
   2y + 5 = 5
   2y = 0
   y = 0

Therefore, the solution is x = -1, y = 0, z = 2.

Answer

Answer

Answer