Three variable equations

Question

x+y+z=73

 

-2x+5y =80

 

x-z=-9

Answer 1

We will use the same substitution and elimination method when working with two variables.

 

 

   x + y + z = 73             eq1

-2x + 5y = 80                 eq2

   x - z = -9                    eq3

 

First, we will solve for z from eq3.

 

-z = -9 - x

 z = x + 9

 

 

Substitute this value of z into eq1.

 

x + y + z = 73

x + y + (x + 9) = 73

x + y + x + 9 = 73

2x + y = 64

 

Now we will work with new eq1 and original eq2.

 

  2x +  y = 64

-2x + 5y = 80

 

 

Lets go on ahead and add these two equations to eliminate the x terms.

 

6y = 144

  y = 24

 

 

Substitute this y value into eq2.

 

-2x + 5y = 80

-2x + 5(24) = 80

-2x + 120 = 80

-2x = -40

   x = 20

 

Substitute this x value into eq3.

 

z = x + 9

z = 20 + 9

z = 29

 

 

Your solutions are

 

x = 20

y = 24

z = 29