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

Determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain w hy not. -3x - 4y + z =- 10
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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.