Question

Which value when placed in the box would result in system of equations which infinitely many solutions y=2x-5 2y-4x=

Answer 1

The value is placed in system of equation is -10.

Explanation:

Given : System of equations
`y=2x-5` and
`2y-4x=?`

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
`y-2x=-5`

The second equation is the first equation multiplied by 2,

i.e.
`2(y-2x)=2(-5)`

`2y-4x=-10`

On comparing the missing term is -10.

Therefore, the value is placed in system of equation is -10.