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

Infinite solutions.

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

`(a_1)/(a_2)=(-5)/(20)=(-1)/(4)\\\\(b_1)/(b_2)=(1)/(-4)=(-1)/(4)\\\\(c_1)/(c_2)=(-2)/(8)=(-1)/(4)`

It means,

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

So, the system of equations has infinite solutions.