Determine the value of each of the variables in the equation below

Question

x+y+z=17

2x+3y-z=38

z=2

Answer 1

x + y + z = 17           eq1

2x + 3y - z = 38         eq2

z = 2                          eq3

 

 

Substitute eq3 into eq1 and eq2.

 

x + y + 2 = 17       

x + y = 15               eq1

 

2x + 3y - 2 = 38    

2x + 3y = 40               eq2

 

 

Next, multiply eq1 coded in orange by 2.  Maintain eq2 coded in green.

 

2x + 2y = 30

2x + 3y = 40

 

 

Subtract the two equations to eliminate the x terms.

 

-y = -10

  y = 10

 

 

Substitute this value of y into eq 1 coded in orange.

 

x = 15 - y

x = 15 - 10

x = 5

 

 

Your solutions are

 

x = 5

y = 10

z = 2