Question

Find solution to the system of linear equations. 5x1 + x2 = 0 , 25x1 + 5x2 = 0

Answer 1

Explanation:

The system of linear equations is expressed as

5x1 + x2 = 0 - - - - - - - - - - - 1

25x1 + 5x2 = 0 - - - - - - - - - - 2

The first step is to eliminate x2 by multiplying equation 1 by 5 and equation 2 by 1. It becomes

25x1 + 5x2 = 0

25x1 + 5x2 = 0

The next step is to subtract equation 2 from equation 1, it becomes

25x1 - 25x1 + 5x2 - 5x2 = 0

0 = 0

The system of equations has an infinite number of solutions. This means that for as many values of x that satisfies equation 1, they will also satisfy equation 2.

Answer 2

the system of equation has infinite solution

Explanation:

`5x_1 + x_2 = 0` ,
`25x_1 + 5x_2 = 0`

Solve the first equation for x_2

Subtract 5x1 on both sides

`5x_1 + x_2 = 0`

`x_2 =-5x_1`

Now substitute -5x1 on second equation

`25x_1 + 5x_2 = 0`

`25x_1 + 5(-5x_1)= 0`

`25x_1-25x_1= 0`

0=0

So the system of equation has infinite solution