Respuesta :
Answer:
The value is placed in system of equation is -10.
Step-by-step explanation:
Given : System of equations [tex]y=2x-5[/tex] and [tex]2y-4x=?[/tex]
To find : Which value when placed in the box (?) would result in system of equations which infinitely many solutions ?
Solution :
For a system of equations to have infinitely many solutions,
The equations have to be linearly dependent i.e. one of the equations is a multiple of the other equation.
In the given system of equations,
The second equation have to be a multiple of the first equation.
Re-write equation 1 as [tex]y-2x=-5[/tex]
The second equation is the first equation multiplied by 2,
i.e. [tex]2(y-2x)=2(-5)[/tex]
[tex]2y-4x=-10[/tex]
On comparing the missing term is -10.
Therefore, the value is placed in system of equation is -10.
