Question

Which value, when placed in the box, would result in a system of equations with infinitly many solutions? Y=2x - 5 2y-4x=

Answer 1

Given:

The system of equations is

`y=2x-5`

`2y-4x=?`

To find:

The missing value for which the given system of equations have infinitely many solutions.

Solution:

Let the missing value be k.

We have,

`y=2x-5`

`2y-4x=k`

Taking all the terms on the left side, the given equations can be rewritten as

`-2x+y+5=0`

`-4x+2y-k=0`

The system of equations
`a_1x+b_1y+c_1=0` and
`a_2x+b_2y+c_2=0` have infinitely many solutions if

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

We have,

`a_1=-2,b_1=1,c_1=5`

`a_2=-4,b_2=2,c_2=-k`

Now,

`(-2)/(-4)=(1)/(2)=(5)/(-k)`

`(1)/(2)=(1)/(2)=(5)/(-k)`

`(1)/(2)=(5)/(-k)`

On cross multiplication, we get

`-k=10`

`k=-10`

Therefore, the missing value is -10.