please help me with this system of equations problem before I go insane the preferable solving methods would be through substitution or elimination

x=8, y=0, z=-3

Step-by-step explanation:

Preferable is substitution because there is less room for mistakes but its long so here goes bare with me on this one :D

Name your equations

4x+2y-5z=47 (first eq)

x-2y+6z=-10 (second eq)

9x-7y-z=75 (third eq)

Lets take the easiest eq to isolate one variable lets take 2nd eq

now this becomes our fourth eq

now again take the easiest eq to isolate another variable lets take the 3rd eq

now this becomes our fifth eq

and now plug in our fifth eq in the fourth eq because we now have z in terms of x and y

and now we got our sixth equation which is x only in terms of y.

now we plug in our sixth equation in our fifth eq to get z in terms of y only

now we have our seventh eq and x &z in terms of just one variable y , now we put equation of z and x which is our sixth eq and seventh eq in our first eq.

and now finally we got y=0 now we need the value of x and z, put the value of y=0 in our seventh eq (z equation)

and now we put the value of y=0 in our sixth eq (x equation)

and now we got all the three values and hence the solution of the system of equation is

x=8, y=0, z=-3

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: