Respuesta :
Answer:
the system of equation has infinite solution
Step-by-step explanation:
[tex]5x_1 + x_2 = 0[/tex] , [tex]25x_1 + 5x_2 = 0[/tex]
Solve the first equation for x_2
Subtract 5x1 on both sides
[tex]5x_1 + x_2 = 0[/tex]
[tex]x_2 =-5x_1[/tex]
Now substitute -5x1 on second equation
[tex]25x_1 + 5x_2 = 0[/tex]
[tex]25x_1 + 5(-5x_1)= 0[/tex]
[tex]25x_1-25x_1= 0[/tex]
0=0
So the system of equation has infinite solution
Answer:
Step-by-step 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.
