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

ediculeN
2021-09-24
Answered

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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avortarF

Answered 2021-09-25
Author has **113** answers

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.

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.

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