Question

2 Points

Find the solution to the system of equations.
X+ y + z= 16
y+ z = 13
z=
5

Answer 1

`z=5\\y=8\\x=3`

Explanation:

`x+y+z=16\\y+z=13\\z=5`

• Maybe switching the order you read this system of equations will help.

`z=5\\y+z=13\\x+y+z=16`

• An important concept in this question is the idea of substitution: if there is a value with a known solution, substituting the known solution in for the original unknown may help solve the equation. I'll show you what I mean with the first step for solving this question.
• Let's look at these two first.

`z=5\\y+z=13`

• Solving for 2 different unknown values in an equation is impossible, so we must get rid of one of the unknowns, thats where
  `z=5` comes into play. If
  `z=5`, then if we substitute
  `5` into our
  `z` value in
  `y+z=13`, then we only have to solve for
  `y`, something that we can pretty easily do.

`z=5\\y+z=13`

`y+5=13\\y+5-5=13-5\\y=8`

OR

`z=5\\z=-y+13`

`5=-y+13\\5-13=-y+13-13\\-8=-y\\y=8`

• The first example above is normal substitution your teacher expects you to do in this question, but I just wanted to show that substitution isn't the only option here.
• Now we know that:

1. 
   `z=5`
2. 
   `y=8`

• Let's solve the last equation here by doing substitution again.

`x+y+z=16\\x+(8)+(5)=16\\x+13=16\\x+13-13=16-13\\x=3`

1. 
   `z=5`
2. 
   `y=8`
3. 
   `x=3`