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

Answer:

Linear-1,2,3,6

Nin-Linear-4,5

Step-by-step 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.