Question

Which statement describes the system of equations?

-5x-4y=-4
25x+ 20y = 20
It has one solution (4,-4).
It has one solution (8,-9).
The system has no solution.
The system has infinitely solutions.

Answer 1

The system has infinitely solutions.

Explanation:

Answer 2

Answer: The system has infinitely solutions.

Explanation:

The given system of equations : -

`-5x-4y=-4\\\Rightarrow\ -5x-4y+4=0-----(1)\\\\25x+ 20y = 20\\\Rightarrow\ 25x+20y-20=0----(2)`

Compare these equation with
`a_1x+b_1y+c_1=0` and
`a_2x+b_2y+c_2=0` respectively , we get

`a_1=-5\ ;b_1=-4\ ;\ c_1=4`

`a_2=25\ ;b_2=20\ ;\ c_2=-20`

Now,
`(a_1)/(a_2)=(-5)/(25)=(-1)/(5)`

`(b_1)/(b_2)=(-4)/(20)=(-1)/(5)`

`(c_1)/(c_2)=(4)/(-20)=(-1)/(5)`

Thus ,
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)=(-1)/(5)`

It means these lines are coincident, thus they have infinite number of solutions.