# Engineering Mechanics - General Principles - Discussion

### Discussion :: General Principles - General Questions (Q.No.4)

4.

Solve the following equation for x, y, and z:

xy + z = –1   –x + y + z = –1   x + 2y – 2z = 5

 [A]. x = 1,      y = 1,      z = –1 [B]. x = 5/3,      y = 7/6,      z = –1/2 [C]. x = –2/3,      y = –2/3,      z = –1 [D]. x = –1,      y = 1,      z = 1

Explanation:

No answer description available for this question.

 Karthik said: (Dec 5, 2010) Substitute each value un the equation whichever satisfies the equation is the answer.

 Arpita Majumder said: (Jan 3, 2011) x-y+z=-1 =>x-y-1+x-y=-1(putting value of z fm 2nd eqn0 =>2(x-y)=0 =>x=y putting x=y in 1st eqn =>z=-1 putting x=y in 3rd eqn =>3x-2z=5 =>x=1(z=-1) as x=1,y=1 hence,x=1,y=1 & z=-1

 Manpreet said: (Feb 19, 2011) First you should put x & y =0 then 0 + z = -1 z = -1 put this in 1 equation it wil x - y = 0 x = y put this in 3 equation x + 2x - 2(-1) = 5 3x + 2 = 5 3x = 3 x = 1 so answer is x = 1 y = 1 z = -1

 Samarth Patel said: (Jun 16, 2011) First 2 equ x-y+z=-1 -x+y+z=-1 solve this equ we get the value of z=-1, now wesolve the last 2 equ and we get the value of y=1, and last we can add the value of y & z in any equ, we can get the x=1 so that we can solve this x=1,y=1,z=-1

 Damodaran said: (Aug 13, 2011) I go with both Manpreet, Samarth Patel because both are right.

 Vikas Mishra said: (Mar 9, 2012) On adding eq. 1&2 we get value of z after finding value of now we add eq 2&3 and putting the value of z and we find the value of why and then we put the value of why &z in eq 1 we find the value of x hence answer is a.

 K.Devika said: (Aug 31, 2012) @Karthik is correct.

 Hamid said: (Jun 21, 2013) x - y + z = -1 -x = -y + z + 1 -x= -1 + (-1) + 1 -x= -1. Minus cancel we get x. ____________________ -x + y + z = -1 -y = -x + z + 1 -y = -1 + (-1) + 1 -y = -2 + 1 = -1 -y = -1. Like x , We cancel minus to get y. _____________________ x + 2y - 2z = 5 2z = x + 2y -5 2z = 1 + (2*1) -5 2z = 3 - 5 z = -2/2 = -1.

 Shaikh Mosin Ahmed said: (Jan 13, 2015) Substitute each value in the equation whichever satisfies the equation is the answer.

 Nayan said: (Apr 21, 2015) x-y+z = -1. -x+y+z = -1. --------------- 2z = -2 (Minus cancel we get 2z). z = -1. (Putting the z = -1). x +2y -2z = 5. -x +y+z = -1. x+2y = 5-2. x+2y = 3. -x+y-1 = -1. -x+y = 0. x+2y = 3. -x+y = 0. ------------. 3y=3. y=1. Putting z = -1, y = 1, we get, x-y+z = -1. x = -1+1-1. x = 1. Therefore, x = 1, y = 1, z = -1.

 Mohit said: (Apr 12, 2016) @Karthik. Your method is wrong for solving the problem because if you putting the values of option D then you also get equal equations.

 @Zikky90 said: (Jun 21, 2016) Using elimination method. Step 1: Sum up eq (1) , (2) and (3). Leaves you with x+2y=3, therefore, x=3-2y. Step 2: Put in value of x in step 1 into eq (3) , therefore z=-1. Step 3: Put value of x in step 1 and z in step 2 into eq (2) , therefore y=1. Step 4: Put in value of why into step 1, therefore x = 1. Answer: x=1, y=1, z=-1.

 Venkatesh said: (Aug 15, 2017) Solve by Cramer's rule (matrix method).

 Manohar H S said: (Apr 1, 2019) I didn't understand this. Please, anyone, explain me.