Question

Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
-5x + y = -2

20x-4y = 8

Answer 1

Answer:

Infinite solutions.

Step-by-step explanation:

The given equations are :

-5x + y = -2 .....(1)

20x-4y = 8 .....(2)

We have,

a₁ = -5, a₂ = 20, b₁ = 1, b₂ = -4, c₁ = -2 and c₂ = 8

$\dfrac{a_1}{a_2}=\dfrac{-5}{20}=\dfrac{-1}{4}\\\\\dfrac{b_1}{b_2}=\dfrac{1}{-4}=\dfrac{-1}{4}\\\\\dfrac{c_1}{c_2}=\dfrac{-2}{8}=\dfrac{-1}{4}$

It means,

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

So, the system of equations has infinite solutions.