Answer:
[tex]z=5\\y=8\\x=3[/tex]
Step-by-step explanation:
[tex]x+y+z=16\\y+z=13\\z=5[/tex]
- Maybe switching the order you read this system of equations will help.
[tex]z=5\\y+z=13\\x+y+z=16[/tex]
- 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.
[tex]z=5\\y+z=13[/tex]
- Solving for 2 different unknown values in an equation is impossible, so we must get rid of one of the unknowns, thats where [tex]z=5[/tex] comes into play. If [tex]z=5[/tex], then if we substitute [tex]5[/tex] into our [tex]z[/tex] value in [tex]y+z=13[/tex], then we only have to solve for [tex]y[/tex], something that we can pretty easily do.
[tex]z=5\\y+z=13[/tex]
[tex]y+5=13\\y+5-5=13-5\\y=8[/tex]
OR
[tex]z=5\\z=-y+13[/tex]
[tex]5=-y+13\\5-13=-y+13-13\\-8=-y\\y=8[/tex]
- 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:
- [tex]z=5[/tex]
- [tex]y=8[/tex]
- Let's solve the last equation here by doing substitution again.
[tex]x+y+z=16\\x+(8)+(5)=16\\x+13=16\\x+13-13=16-13\\x=3[/tex]
- [tex]z=5[/tex]
- [tex]y=8[/tex]
- [tex]x=3[/tex]
