X+y+z=9
2x-2y+4z =0

find the solution set of the linear system. write solution using a parameter

x=-3y+18

z=2y-9.

Step-by-step explanation:

x+y+z=9 , which means that x=9-y-z.

2x-2y+4z=0, which, by dividing both sides by 2, means that x-y+2z=0.

Substituting x from the first formula we have (9-y-z)-y+2z=0, which means that z=2y-9. Using the formula for x we have x=9-y-z=9-y-(2y-9)=-3y+18.

So our solutions, using y as a parameter, are x=-3y+18 and z=2y-9.

We can verify if this is true (and no mistakes were done in the derivation) by substituting in the original formulas:

x+y+z=(-3y+18)+y+(2y-9)=9, which we know must be true, and

2(-3y+18)-2y+4(2y-9)=-6y+36-2y+8y-36=0, which we know must be true.

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

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step-by-step explanation: