Question

What are your solutions when you solve for this System? It's really tricky...

x+y=9
y+z=7
x-z=2

Answer 1

x = 9-y
x = 2+z
9-y = 2+z
7 -y = z
y+ (7-y) = 7 no solution here
need someone to double check

Answer 2

jayz657,

y+ (7-y) = 7

turns into

y - y + 7 = 7

which turns into

7 = 7

which is ALWAYS TRUE regardless of what x, y and z are.

Answer 3

so there are actually an infinite number of solutions

Answer 4

oh right haha there you go

Answer 5

So does that mean theres no 3 speciffic answerss?

Answer 6

depending on how your teacher wants it, the answer is either


a) you just say there are infinitely many solutions

or

b) you say there are infinitely many solutions and that the system is consistent and dependent

or

c) you write the solution as an ordered triple in the form (x,y,z) where you introduce a free variable (eg: z is a free variable where x and y depend on z)

Answer 7

If you must answer as described in c) above, then


y+z=7 ---> y = 7 - z

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

x+y=9 ----> x = 9-y ----> x = 9-(7-z) ----> x = 2 - z


So if z is the free variable, then the solution as an ordered triple is ( 2-z, 7-z, z)

Answer 8

If z = 0, then ( 2-z, 7-z, z) becomes ( 2, 7, 0), which is one solution

If z = 1, then ( 2-z, 7-z, z) becomes ( 1, 6, 1), which is another solution

If z = 2, then ( 2-z, 7-z, z) becomes ( 0, 5, 2), which is another solution

etc etc

You can replace z with any real number to get any solution (of the infinitely many solutions)

Answer 9

ok thnx!

Answer 10

np