Question

Determine if each equation is a linear equation.

[Linear equation / Not a linear equation]
1)
`5x_1 + x_2 - 7x_3 = 4`
2)
`5x_1 + 4.6x_2 + 12x_3 = -5`
3)
`3x_1 - x_3 = -5x_2 + 7`
4)
`3x_1x_2 + x_3 = 5`
5)
`4x_1^3 + x_2 = 5`
6)
`6x_1 - 4x_2 + x_3 = 0`

Answer 1

Linear-1,2,3,6

Nin-Linear-4,5

Explanation:

A linear equation is an equation in which the highest power of the variable is 1.

Out of the given equations, the following are linear.

1)
`5x_1 + x_2 - 7x_3 = 4`

2)
`5x_1 + 4.6x_2 + 12x_3 = -5`

3)
`3x_1 - x_3 = -5x_2 + 7`

6)
`6x_1 - 4x_2 + x_3 = 0`

These equations on the other hand are nonlinear.

4)
`3x_1x_2 + x_3 = 5`

5)
`4x_1^3 + x_2 = 5`

No 4 contains a term which is the product of two variables therefore it is not linear.

No 5 contains a term whose highest power is 3. Such an equation is a Cubic Equation.