Determine which equations are linear equations in the variables x, y, and z. If

Step 1
The general form of linear equation in three variables x, y and z is:
ax+by+cz=d...(i)
Where, a, b and c non-zero numbers.
The given equation is
−3x−4y+z=−10...(ii)
We need to check whether the given equation is linear or not.
Step 2
In the given equation the powers of all the variables are 1.
The given equation is in the form of ax+by+cz=d.
On comparing (i) and (ii), we get
a=−3, b=−4, c=1
Here, a, b and c are non-zero numbers. So, the given equation is linear.
Step 3
Answer: Yes, the given equation −3x−4y+z=−10 is a linear equation in three variables x, y and z.