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

Answer: The system has infinitely solutions.

Step-by-step 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, $\dfrac{a_1}{a_2}=\dfrac{-5}{25}=\dfrac{-1}{5}$

$\dfrac{b_1}{b_2}=\dfrac{-4}{20}=\dfrac{-1}{5}$

$\dfrac{c_1}{c_2}=\dfrac{4}{-20}=\dfrac{-1}{5}$

Thus , $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{-1}{5}$

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