Work out the system

Question

2x + 4y+ 3z=10

2x +3y+11z=23

4y-2z=15

Answer 1

2x + 4y+ 3z=10    {equation 1}
2x +3y+11z=23    {equation 2}
4y-2z=15              {equation 3}

 

Let's use elimination to get 2 equations with 2 unknowns.  The

easiest variable to eliminate is x.  Subtract equation 2 from equation 1

 

  2x + 4y +   3z  = 10

-(2x + 3y + 11z = 23)

--------------------------

          y - 8z = -13     {equation 4}

 

4y - 2z  = 15    {equation 3}

 y -  8z = -13   |{equation 4}

 

multiply equation 4 by -4 and add these two equations

 

  4y - 2z = 15

-4y + 32z = 52

---------------------

        30z = 67

          z = 67/30

 

Given 4y - 2z = 15 and z = 67/30

4y - 2(67/30) = 15

4y - 67/15 = 15

60y - 67 = 225

60y = 291

y = 291/60 = 97/20 

 

From equation 1: 2x + 4y+ 3z=10    

2x + 4(97/20) + 3(67/30) = 10

2x + 97/5 + 67/10 = 10

20x + 194 + 67 = 100

20x + 261 = 100

20x = -161

x = -161/20